Home Metamath Proof ExplorerTheorem List (p. 276 of 311) < Previous  Next > Browser slow? Try the Unicode version.

 Color key: Metamath Proof Explorer (1-21328) Hilbert Space Explorer (21329-22851) Users' Mathboxes (22852-31058)

Theorem List for Metamath Proof Explorer - 27501-27600   *Has distinct variable group(s)
TypeLabelDescription
Statement

Syntaxw-bnj13 27501 Extend wff notation with the following predicate: is set-like on . (New usage is discouraged.)

Definitiondf-bnj13 27502* Define the following predicate: is set-like on . (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Syntaxw-bnj15 27503 Extend wff notation with the following predicate: is both well-founded and set-like on . (New usage is discouraged.)

Definitiondf-bnj15 27504 Define the following predicate: is both well-founded and set-like on . (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Syntaxc-bnj18 27505 Extend class notation with the function giving: the transitive closure of in by . (New usage is discouraged.)

Definitiondf-bnj18 27506* Define the function giving: the transitive closure of in by . This definition has been designed for facilitating verification that it is eliminable and that the \$d restrictions are sound and complete. For a more readable definition see bnj882 27744. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Syntaxw-bnj19 27507 Extend wff notation with the following predicate: is transitive for and . (New usage is discouraged.)

Definitiondf-bnj19 27508* Define the following predicate: is transitive for and . (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

16.22.1  First order logic and set theory

Theorembnj170 27509 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (New usage is discouraged.)

Theorembnj240 27510 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj248 27511 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj250 27512 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj251 27513 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj252 27514 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj253 27515 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj255 27516 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj256 27517 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj257 27518 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj258 27519 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj268 27520 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj290 27521 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj291 27522 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj312 27523 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj334 27524 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (New usage is discouraged.)

Theorembnj345 27525 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (New usage is discouraged.)

Theorembnj422 27526 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (New usage is discouraged.)

Theorembnj432 27527 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj446 27528 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj21 27529* First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj23 27530* First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Mario Carneiro, 22-Dec-2016.) (New usage is discouraged.)

Theorembnj31 27531 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj62 27532* First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj89 27533* First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj90 27534* First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Mario Carneiro, 22-Dec-2016.) (New usage is discouraged.)

Theorembnj101 27535 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj105 27536 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj115 27537 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj132 27538* First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) (New usage is discouraged.)

Theorembnj133 27539 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj142 27540 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Mario Carneiro, 22-Dec-2016.) (New usage is discouraged.)

Theorembnj145 27541 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj156 27542 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj158 27543* First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj168 27544* First-order logic and set theory. Revised to remove dependence on ax-reg 7190. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Revised by NM, 21-Dec-2016.) (New usage is discouraged.)

Theorembnj206 27545 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj216 27546 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj219 27547 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj226 27548* First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj228 27549 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) (New usage is discouraged.)

Theorembnj519 27550 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Revised by Mario Carneiro, 6-May-2015.) (New usage is discouraged.)

Theorembnj521 27551 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj524 27552 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj525 27553* First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj534 27554* First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj538 27555* First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj529 27556 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj551 27557 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj563 27558 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj564 27559 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj593 27560 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj596 27561 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj610 27562* Pass from equality ( ) to substitution ( ) without the distinct variable restriction (\$d ). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj642 27563 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj643 27564 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj645 27565 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj658 27566 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj667 27567 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj705 27568 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj706 27569 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj707 27570 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj708 27571 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj721 27572 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj832 27573 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj833 27574 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj835 27575 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj836 27576 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj837 27577 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj769 27578 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj770 27579 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj771 27580 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj887 27581 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj918 27582 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj919 27583* First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj923 27584 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj926 27585 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj927 27586 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj930 27587 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj931 27588 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj937 27589* First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj941 27590 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj945 27591 Technical lemma for bnj69 27826. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj946 27592 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj951 27593 -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj956 27594 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj976 27595* First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj982 27596 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj1019 27597* First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj1023 27598 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj1095 27599 First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Theorembnj1096 27600* First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

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 30801-30900 310 30901-31000 311 31001-31058
 Copyright terms: Public domain < Previous  Next >