Home Metamath Proof ExplorerTheorem List (p. 27 of 309) < Previous  Next > Browser slow? Try the Unicode version.

 Color key: Metamath Proof Explorer (1-21328) Hilbert Space Explorer (21329-22851) Users' Mathboxes (22852-30843)

Theorem List for Metamath Proof Explorer - 2601-2700   *Has distinct variable group(s)
TypeLabelDescription
Statement

Theoremrgen2 2601* Generalization rule for restricted quantification. (Contributed by NM, 30-May-1999.)

Theoremrgen3 2602* Generalization rule for restricted quantification. (Contributed by NM, 12-Jan-2008.)

Theoremr19.21bi 2603 Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 20-Nov-1994.)

Theoremrspec2 2604 Specialization rule for restricted quantification. (Contributed by NM, 20-Nov-1994.)

Theoremrspec3 2605 Specialization rule for restricted quantification. (Contributed by NM, 20-Nov-1994.)

Theoremr19.21be 2606 Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 21-Nov-1994.)

Theoremnrex 2607 Inference adding restricted existential quantifier to negated wff. (Contributed by NM, 16-Oct-2003.)

Theoremnrexdv 2608* Deduction adding restricted existential quantifier to negated wff. (Contributed by NM, 16-Oct-2003.)

Theoremrexim 2609 Theorem 19.22 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 22-Nov-1994.) (Proof shortened by Andrew Salmon, 30-May-2011.)

Theoremreximia 2610 Inference quantifying both antecedent and consequent. (Contributed by NM, 10-Feb-1997.)

Theoremreximi2 2611 Inference quantifying both antecedent and consequent, based on Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 8-Nov-2004.)

Theoremreximi 2612 Inference quantifying both antecedent and consequent. (Contributed by NM, 18-Oct-1996.)

Theoremreximdai 2613 Deduction from Theorem 19.22 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 31-Aug-1999.)

Theoremreximdv2 2614* Deduction quantifying both antecedent and consequent, based on Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 17-Sep-2003.)

Theoremreximdvai 2615* Deduction quantifying both antecedent and consequent, based on Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 14-Nov-2002.)

Theoremreximdv 2616* Deduction from Theorem 19.22 of [Margaris] p. 90. (Restricted quantifier version with strong hypothesis.) (Contributed by NM, 24-Jun-1998.)

Theoremreximdva 2617* Deduction quantifying both antecedent and consequent, based on Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 22-May-1999.)

Theoremr19.12 2618* Theorem 19.12 of [Margaris] p. 89 with restricted quantifiers. (Contributed by NM, 15-Oct-2003.) (Proof shortened by Andrew Salmon, 30-May-2011.)

Theoremr19.23t 2619 Closed theorem form of r19.23 2620. (Contributed by NM, 4-Mar-2013.) (Revised by Mario Carneiro, 8-Oct-2016.)

Theoremr19.23 2620 Theorem 19.23 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 22-Oct-2010.) (Proof shortened by Mario Carneiro, 8-Oct-2016.)

Theoremr19.23v 2621* Theorem 19.23 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 31-Aug-1999.)

Theoremrexlimi 2622 Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 30-Nov-2003.) (Proof shortened by Andrew Salmon, 30-May-2011.)

Theoremrexlimiv 2623* Inference from Theorem 19.23 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 20-Nov-1994.)

Theoremrexlimiva 2624* Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 18-Dec-2006.)

Theoremrexlimivw 2625* Weaker version of rexlimiv 2623. (Contributed by FL, 19-Sep-2011.)

Theoremrexlimd 2626 Deduction from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 27-May-1998.) (Proof shortened by Andrew Salmon, 30-May-2011.)

Theoremrexlimd2 2627 Version of rexlimd 2626 with deduction version of second hypothesis. (Contributed by NM, 21-Jul-2013.) (Revised by Mario Carneiro, 8-Oct-2016.)

Theoremrexlimdv 2628* Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 14-Nov-2002.) (Proof shortened by Eric Schmidt, 22-Dec-2006.)

Theoremrexlimdva 2629* Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 20-Jan-2007.)

Theoremrexlimdvaa 2630* Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by Mario Carneiro, 15-Jun-2016.)

Theoremrexlimdv3a 2631* Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). Frequently-used variant of rexlimdv 2628. (Contributed by NM, 7-Jun-2015.)

Theoremrexlimdvw 2632* Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 18-Jun-2014.)

Theoremrexlimddv 2633* Restricted existential elimination rule of natural deduction. (Contributed by Mario Carneiro, 15-Jun-2016.)

Theoremrexlimivv 2634* Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 17-Feb-2004.)

Theoremrexlimdvv 2635* Inference from Theorem 19.23 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 22-Jul-2004.)

Theoremrexlimdvva 2636* Inference from Theorem 19.23 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 18-Jun-2014.)

Theoremr19.26 2637 Theorem 19.26 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 28-Jan-1997.) (Proof shortened by Andrew Salmon, 30-May-2011.)

Theoremr19.26-2 2638 Theorem 19.26 of [Margaris] p. 90 with 2 restricted quantifiers. (Contributed by NM, 10-Aug-2004.)

Theoremr19.26-3 2639 Theorem 19.26 of [Margaris] p. 90 with 3 restricted quantifiers. (Contributed by FL, 22-Nov-2010.)

Theoremr19.26m 2640 Theorem 19.26 of [Margaris] p. 90 with mixed quantifiers. (Contributed by NM, 22-Feb-2004.)

Theoremralbi 2641 Distribute a restricted universal quantifier over a biconditional. Theorem 19.15 of [Margaris] p. 90 with restricted quantification. (Contributed by NM, 6-Oct-2003.)

Theoremralbiim 2642 Split a biconditional and distribute quantifier. (Contributed by NM, 3-Jun-2012.)

Theoremr19.27av 2643* Restricted version of one direction of Theorem 19.27 of [Margaris] p. 90. (The other direction doesn't hold when is empty.) (Contributed by NM, 3-Jun-2004.) (Proof shortened by Andrew Salmon, 30-May-2011.)

Theoremr19.28av 2644* Restricted version of one direction of Theorem 19.28 of [Margaris] p. 90. (The other direction doesn't hold when is empty.) (Contributed by NM, 2-Apr-2004.)

Theoremr19.29 2645 Theorem 19.29 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 31-Aug-1999.) (Proof shortened by Andrew Salmon, 30-May-2011.)

Theoremr19.29r 2646 Variation of Theorem 19.29 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 31-Aug-1999.)

Theoremr19.30 2647 Theorem 19.30 of [Margaris] p. 90 with restricted quantifiers. (Contributed by Scott Fenton, 25-Feb-2011.)

Theoremr19.32v 2648* Theorem 19.32 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 25-Nov-2003.)

Theoremr19.35 2649 Restricted quantifier version of Theorem 19.35 of [Margaris] p. 90. (Contributed by NM, 20-Sep-2003.)

Theoremr19.36av 2650* One direction of a restricted quantifier version of Theorem 19.36 of [Margaris] p. 90. The other direction doesn't hold when is empty. (Contributed by NM, 22-Oct-2003.)

Theoremr19.37 2651 Restricted version of one direction of Theorem 19.37 of [Margaris] p. 90. (The other direction doesn't hold when is empty.) (Contributed by FL, 13-May-2012.) (Revised by Mario Carneiro, 11-Dec-2016.)

Theoremr19.37av 2652* Restricted version of one direction of Theorem 19.37 of [Margaris] p. 90. (The other direction doesn't hold when is empty.) (Contributed by NM, 2-Apr-2004.)

Theoremr19.40 2653 Restricted quantifier version of Theorem 19.40 of [Margaris] p. 90. (Contributed by NM, 2-Apr-2004.)

Theoremr19.41 2654 Restricted quantifier version of Theorem 19.41 of [Margaris] p. 90. (Contributed by NM, 1-Nov-2010.)

Theoremr19.41v 2655* Restricted quantifier version of Theorem 19.41 of [Margaris] p. 90. (Contributed by NM, 17-Dec-2003.)

Theoremr19.42v 2656* Restricted version of Theorem 19.42 of [Margaris] p. 90. (Contributed by NM, 27-May-1998.)

Theoremr19.43 2657 Restricted version of Theorem 19.43 of [Margaris] p. 90. (Contributed by NM, 27-May-1998.) (Proof shortened by Andrew Salmon, 30-May-2011.)

Theoremr19.44av 2658* One direction of a restricted quantifier version of Theorem 19.44 of [Margaris] p. 90. The other direction doesn't hold when is empty. (Contributed by NM, 2-Apr-2004.)

Theoremr19.45av 2659* Restricted version of one direction of Theorem 19.45 of [Margaris] p. 90. (The other direction doesn't hold when is empty.) (Contributed by NM, 2-Apr-2004.)

Theoremralcomf 2660* Commutation of restricted quantifiers. (Contributed by Mario Carneiro, 14-Oct-2016.)

Theoremrexcomf 2661* Commutation of restricted quantifiers. (Contributed by Mario Carneiro, 14-Oct-2016.)

Theoremralcom 2662* Commutation of restricted quantifiers. (Contributed by NM, 13-Oct-1999.) (Revised by Mario Carneiro, 14-Oct-2016.)

Theoremrexcom 2663* Commutation of restricted quantifiers. (Contributed by NM, 19-Nov-1995.) (Revised by Mario Carneiro, 14-Oct-2016.)

Theoremrexcom13 2664* Swap 1st and 3rd restricted existential quantifiers. (Contributed by NM, 8-Apr-2015.)

Theoremrexrot4 2665* Rotate existential restricted quantifiers twice. (Contributed by NM, 8-Apr-2015.)

Theoremralcom2 2666* Commutation of restricted quantifiers. Note that and needn't be distinct (this makes the proof longer). (Contributed by NM, 24-Nov-1994.) (Proof shortened by Mario Carneiro, 17-Oct-2016.)

Theoremralcom3 2667 A commutative law for restricted quantifiers that swaps the domain of the restriction. (Contributed by NM, 22-Feb-2004.)

Theoremreean 2668* Rearrange existential quantifiers. (Contributed by NM, 27-Oct-2010.) (Proof shortened by Andrew Salmon, 30-May-2011.)

Theoremreeanv 2669* Rearrange existential quantifiers. (Contributed by NM, 9-May-1999.)

Theorem3reeanv 2670* Rearrange three existential quantifiers. (Contributed by Jeff Madsen, 11-Jun-2010.)

Theorem2ralor 2671* Distribute quantification over "or". (Contributed by Jeff Madsen, 19-Jun-2010.)

Theoremnfreu1 2672 is not free in . (Contributed by NM, 19-Mar-1997.)

Theoremnfreud 2673 Deduction version of nfreu 2674. (Contributed by NM, 15-Feb-2013.) (Revised by Mario Carneiro, 8-Oct-2016.)

Theoremnfreu 2674 Bound-variable hypothesis builder for restricted uniqueness. (Contributed by NM, 30-Oct-2010.) (Revised by Mario Carneiro, 8-Oct-2016.)

Theoremrabid 2675 An "identity" law of concretion for restricted abstraction. Special case of Definition 2.1 of [Quine] p. 16. (Contributed by NM, 9-Oct-2003.)

Theoremrabid2 2676* An "identity" law for restricted class abstraction. (Contributed by NM, 9-Oct-2003.) (Proof shortened by Andrew Salmon, 30-May-2011.)

Theoremrabbi 2677 Equivalent wff's correspond to equal restricted class abstractions. Closed theorem form of rabbidva 2718. (Contributed by NM, 25-Nov-2013.)

Theoremrabswap 2678 Swap with a membership relation in a restricted class abstraction. (Contributed by NM, 4-Jul-2005.)

Theoremnfrab1 2679 The abstraction variable in a restricted class abstraction isn't free. (Contributed by NM, 19-Mar-1997.)

Theoremnfrab 2680 A variable not free in a wff remains so in a restricted class abstraction. (Contributed by NM, 13-Oct-2003.) (Revised by Mario Carneiro, 9-Oct-2016.)

Theoremreubida 2681 Formula-building rule for restricted existential quantifier (deduction rule). (Contributed by Mario Carneiro, 19-Nov-2016.)

Theoremreubidva 2682* Formula-building rule for restricted existential quantifier (deduction rule). (Contributed by NM, 13-Nov-2004.)

Theoremreubidv 2683* Formula-building rule for restricted existential quantifier (deduction rule). (Contributed by NM, 17-Oct-1996.)

Theoremreubiia 2684 Formula-building rule for restricted existential quantifier (inference rule). (Contributed by NM, 14-Nov-2004.)

Theoremreubii 2685 Formula-building rule for restricted existential quantifier (inference rule). (Contributed by NM, 22-Oct-1999.)

Theoremraleqf 2686 Equality theorem for restricted universal quantifier, with bound-variable hypotheses instead of distinct variable restrictions. (Contributed by NM, 7-Mar-2004.) (Revised by Andrew Salmon, 11-Jul-2011.)

Theoremrexeqf 2687 Equality theorem for restricted existential quantifier, with bound-variable hypotheses instead of distinct variable restrictions. (Contributed by NM, 9-Oct-2003.) (Revised by Andrew Salmon, 11-Jul-2011.)

Theoremreueq1f 2688 Equality theorem for restricted uniqueness quantifier, with bound-variable hypotheses instead of distinct variable restrictions. (Contributed by NM, 5-Apr-2004.) (Revised by Andrew Salmon, 11-Jul-2011.)

Theoremraleq 2689* Equality theorem for restricted universal quantifier. (Contributed by NM, 16-Nov-1995.)

Theoremrexeq 2690* Equality theorem for restricted existential quantifier. (Contributed by NM, 29-Oct-1995.)

Theoremreueq1 2691* Equality theorem for restricted uniqueness quantifier. (Contributed by NM, 5-Apr-2004.)

Theoremraleqi 2692* Equality inference for restricted universal qualifier. (Contributed by Paul Chapman, 22-Jun-2011.)

Theoremrexeqi 2693* Equality inference for restricted existential qualifier. (Contributed by Mario Carneiro, 23-Apr-2015.)

Theoremraleqdv 2694* Equality deduction for restricted universal quantifier. (Contributed by NM, 13-Nov-2005.)

Theoremrexeqdv 2695* Equality deduction for restricted existential quantifier. (Contributed by NM, 14-Jan-2007.)

Theoremraleqbi1dv 2696* Equality deduction for restricted universal quantifier. (Contributed by NM, 16-Nov-1995.)

Theoremrexeqbi1dv 2697* Equality deduction for restricted existential quantifier. (Contributed by NM, 18-Mar-1997.)

Theoremreueqd 2698* Equality deduction for restricted uniqueness quantifier. (Contributed by NM, 5-Apr-2004.)

Theoremraleqbidv 2699* Equality deduction for restricted universal quantifier. (Contributed by NM, 6-Nov-2007.)

Theoremrexeqbidv 2700* Equality deduction for restricted universal quantifier. (Contributed by NM, 6-Nov-2007.)

Page List
Jump to page: Contents  1 1-100 2 101-200 3 201-300 4 301-400 5 401-500 6 501-600 7 601-700 8 701-800 9 801-900 10 901-1000 11 1001-1100 12 1101-1200 13 1201-1300 14 1301-1400 15 1401-1500 16 1501-1600 17 1601-1700 18 1701-1800 19 1801-1900 20 1901-2000 21 2001-2100 22 2101-2200 23 2201-2300 24 2301-2400 25 2401-2500 26 2501-2600 27 2601-2700 28 2701-2800 29 2801-2900 30 2901-3000 31 3001-3100 32 3101-3200 33 3201-3300 34 3301-3400 35 3401-3500 36 3501-3600 37 3601-3700 38 3701-3800 39 3801-3900 40 3901-4000 41 4001-4100 42 4101-4200 43 4201-4300 44 4301-4400 45 4401-4500 46 4501-4600 47 4601-4700 48 4701-4800 49 4801-4900 50 4901-5000 51 5001-5100 52 5101-5200 53 5201-5300 54 5301-5400 55 5401-5500 56 5501-5600 57 5601-5700 58 5701-5800 59 5801-5900 60 5901-6000 61 6001-6100 62 6101-6200 63 6201-6300 64 6301-6400 65 6401-6500 66 6501-6600 67 6601-6700 68 6701-6800 69 6801-6900 70 6901-7000 71 7001-7100 72 7101-7200 73 7201-7300 74 7301-7400 75 7401-7500 76 7501-7600 77 7601-7700 78 7701-7800 79 7801-7900 80 7901-8000 81 8001-8100 82 8101-8200 83 8201-8300 84 8301-8400 85 8401-8500 86 8501-8600 87 8601-8700 88 8701-8800 89 8801-8900 90 8901-9000 91 9001-9100 92 9101-9200 93 9201-9300 94 9301-9400 95 9401-9500 96 9501-9600 97 9601-9700 98 9701-9800 99 9801-9900 100 9901-10000 101 10001-10100 102 10101-10200 103 10201-10300 104 10301-10400 105 10401-10500 106 10501-10600 107 10601-10700 108 10701-10800 109 10801-10900 110 10901-11000 111 11001-11100 112 11101-11200 113 11201-11300 114 11301-11400 115 11401-11500 116 11501-11600 117 11601-11700 118 11701-11800 119 11801-11900 120 11901-12000 121 12001-12100 122 12101-12200 123 12201-12300 124 12301-12400 125 12401-12500 126 12501-12600 127 12601-12700 128 12701-12800 129 12801-12900 130 12901-13000 131 13001-13100 132 13101-13200 133 13201-13300 134 13301-13400 135 13401-13500 136 13501-13600 137 13601-13700 138 13701-13800 139 13801-13900 140 13901-14000 141 14001-14100 142 14101-14200 143 14201-14300 144 14301-14400 145 14401-14500 146 14501-14600 147 14601-14700 148 14701-14800 149 14801-14900 150 14901-15000 151 15001-15100 152 15101-15200 153 15201-15300 154 15301-15400 155 15401-15500 156 15501-15600 157 15601-15700 158 15701-15800 159 15801-15900 160 15901-16000 161 16001-16100 162 16101-16200 163 16201-16300 164 16301-16400 165 16401-16500 166 16501-16600 167 16601-16700 168 16701-16800 169 16801-16900 170 16901-17000 171 17001-17100 172 17101-17200 173 17201-17300 174 17301-17400 175 17401-17500 176 17501-17600 177 17601-17700 178 17701-17800 179 17801-17900 180 17901-18000 181 18001-18100 182 18101-18200 183 18201-18300 184 18301-18400 185 18401-18500 186 18501-18600 187 18601-18700 188 18701-18800 189 18801-18900 190 18901-19000 191 19001-19100 192 19101-19200 193 19201-19300 194 19301-19400 195 19401-19500 196 19501-19600 197 19601-19700 198 19701-19800 199 19801-19900 200 19901-20000 201 20001-20100 202 20101-20200 203 20201-20300 204 20301-20400 205 20401-20500 206 20501-20600 207 20601-20700 208 20701-20800 209 20801-20900 210 20901-21000 211 21001-21100 212 21101-21200 213 21201-21300 214 21301-21400 215 21401-21500 216 21501-21600 217 21601-21700 218 21701-21800 219 21801-21900 220 21901-22000 221 22001-22100 222 22101-22200 223 22201-22300 224 22301-22400 225 22401-22500 226 22501-22600 227 22601-22700 228 22701-22800 229 22801-22900 230 22901-23000 231 23001-23100 232 23101-23200 233 23201-23300 234 23301-23400 235 23401-23500 236 23501-23600 237 23601-23700 238 23701-23800 239 23801-23900 240 23901-24000 241 24001-24100 242 24101-24200 243 24201-24300 244 24301-24400 245 24401-24500 246 24501-24600 247 24601-24700 248 24701-24800 249 24801-24900 250 24901-25000 251 25001-25100 252 25101-25200 253 25201-25300 254 25301-25400 255 25401-25500 256 25501-25600 257 25601-25700 258 25701-25800 259 25801-25900 260 25901-26000 261 26001-26100 262 26101-26200 263 26201-26300 264 26301-26400 265 26401-26500 266 26501-26600 267 26601-26700 268 26701-26800 269 26801-26900 270 26901-27000 271 27001-27100 272 27101-27200 273 27201-27300 274 27301-27400 275 27401-27500 276 27501-27600 277 27601-27700 278 27701-27800 279 27801-27900 280 27901-28000 281 28001-28100 282 28101-28200 283 28201-28300 284 28301-28400 285 28401-28500 286 28501-28600 287 28601-28700 288 28701-28800 289 28801-28900 290 28901-29000 291 29001-29100 292 29101-29200 293 29201-29300 294 29301-29400 295 29401-29500 296 29501-29600 297 29601-29700 298 29701-29800 299 29801-29900 300 29901-30000 301 30001-30100 302 30101-30200 303 30201-30300 304 30301-30400 305 30401-30500 306 30501-30600 307 30601-30700 308 30701-30800 309 30801-30843
 Copyright terms: Public domain < Previous  Next >