HomeHome Intuitionistic Logic Explorer
Theorem List (p. 12 of 75)
< Previous  Next >
Bad symbols? Try the
GIF version.

Mirrors  >  Metamath Home Page  >  ILE Home Page  >  Theorem List Contents  >  Recent Proofs       This page: Page List

Theorem List for Intuitionistic Logic Explorer - 1101-1200   *Has distinct variable group(s)
TypeLabelDescription
Statement
 
Theorem3imp1 1101 Importation to left triple conjunction. (Contributed by NM, 24-Feb-2005.)
(φ → (ψ → (χ → (θτ))))       (((φ ψ χ) θ) → τ)
 
Theorem3impd 1102 Importation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)
(φ → (ψ → (χ → (θτ))))       (φ → ((ψ χ θ) → τ))
 
Theorem3imp2 1103 Importation to right triple conjunction. (Contributed by NM, 26-Oct-2006.)
(φ → (ψ → (χ → (θτ))))       ((φ (ψ χ θ)) → τ)
 
Theorem3exp1 1104 Exportation from left triple conjunction. (Contributed by NM, 24-Feb-2005.)
(((φ ψ χ) θ) → τ)       (φ → (ψ → (χ → (θτ))))
 
Theorem3expd 1105 Exportation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)
(φ → ((ψ χ θ) → τ))       (φ → (ψ → (χ → (θτ))))
 
Theorem3exp2 1106 Exportation from right triple conjunction. (Contributed by NM, 26-Oct-2006.)
((φ (ψ χ θ)) → τ)       (φ → (ψ → (χ → (θτ))))
 
Theoremexp5o 1107 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)
((φ ψ χ) → ((θ τ) → η))       (φ → (ψ → (χ → (θ → (τη)))))
 
Theoremexp516 1108 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)
(((φ (ψ χ θ)) τ) → η)       (φ → (ψ → (χ → (θ → (τη)))))
 
Theoremexp520 1109 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)
(((φ ψ χ) (θ τ)) → η)       (φ → (ψ → (χ → (θ → (τη)))))
 
Theorem3anassrs 1110 Associative law for conjunction applied to antecedent (eliminates syllogism). (Contributed by Mario Carneiro, 4-Jan-2017.)
((φ (ψ χ θ)) → τ)       ((((φ ψ) χ) θ) → τ)
 
Theorem3adant1l 1111 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
((φ ψ χ) → θ)       (((τ φ) ψ χ) → θ)
 
Theorem3adant1r 1112 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
((φ ψ χ) → θ)       (((φ τ) ψ χ) → θ)
 
Theorem3adant2l 1113 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
((φ ψ χ) → θ)       ((φ (τ ψ) χ) → θ)
 
Theorem3adant2r 1114 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
((φ ψ χ) → θ)       ((φ (ψ τ) χ) → θ)
 
Theorem3adant3l 1115 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
((φ ψ χ) → θ)       ((φ ψ (τ χ)) → θ)
 
Theorem3adant3r 1116 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
((φ ψ χ) → θ)       ((φ ψ (χ τ)) → θ)
 
Theoremsyl12anc 1117 Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009.)
(φψ)    &   (φχ)    &   (φθ)    &   ((ψ (χ θ)) → τ)       (φτ)
 
Theoremsyl21anc 1118 Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009.)
(φψ)    &   (φχ)    &   (φθ)    &   (((ψ χ) θ) → τ)       (φτ)
 
Theoremsyl3anc 1119 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   ((ψ χ θ) → τ)       (φτ)
 
Theoremsyl22anc 1120 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (((ψ χ) (θ τ)) → η)       (φη)
 
Theoremsyl13anc 1121 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   ((ψ (χ θ τ)) → η)       (φη)
 
Theoremsyl31anc 1122 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (((ψ χ θ) τ) → η)       (φη)
 
Theoremsyl112anc 1123 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   ((ψ χ (θ τ)) → η)       (φη)
 
Theoremsyl121anc 1124 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   ((ψ (χ θ) τ) → η)       (φη)
 
Theoremsyl211anc 1125 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (((ψ χ) θ τ) → η)       (φη)
 
Theoremsyl23anc 1126 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (((ψ χ) (θ τ η)) → ζ)       (φζ)
 
Theoremsyl32anc 1127 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (((ψ χ θ) (τ η)) → ζ)       (φζ)
 
Theoremsyl122anc 1128 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   ((ψ (χ θ) (τ η)) → ζ)       (φζ)
 
Theoremsyl212anc 1129 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (((ψ χ) θ (τ η)) → ζ)       (φζ)
 
Theoremsyl221anc 1130 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (((ψ χ) (θ τ) η) → ζ)       (φζ)
 
Theoremsyl113anc 1131 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   ((ψ χ (θ τ η)) → ζ)       (φζ)
 
Theoremsyl131anc 1132 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   ((ψ (χ θ τ) η) → ζ)       (φζ)
 
Theoremsyl311anc 1133 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (((ψ χ θ) τ η) → ζ)       (φζ)
 
Theoremsyl33anc 1134 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   (((ψ χ θ) (τ η ζ)) → σ)       (φσ)
 
Theoremsyl222anc 1135 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   (((ψ χ) (θ τ) (η ζ)) → σ)       (φσ)
 
Theoremsyl123anc 1136 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   ((ψ (χ θ) (τ η ζ)) → σ)       (φσ)
 
Theoremsyl132anc 1137 Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   ((ψ (χ θ τ) (η ζ)) → σ)       (φσ)
 
Theoremsyl213anc 1138 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   (((ψ χ) θ (τ η ζ)) → σ)       (φσ)
 
Theoremsyl231anc 1139 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   (((ψ χ) (θ τ η) ζ) → σ)       (φσ)
 
Theoremsyl312anc 1140 Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   (((ψ χ θ) τ (η ζ)) → σ)       (φσ)
 
Theoremsyl321anc 1141 Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   (((ψ χ θ) (τ η) ζ) → σ)       (φσ)
 
Theoremsyl133anc 1142 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   (φσ)    &   ((ψ (χ θ τ) (η ζ σ)) → ρ)       (φρ)
 
Theoremsyl313anc 1143 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   (φσ)    &   (((ψ χ θ) τ (η ζ σ)) → ρ)       (φρ)
 
Theoremsyl331anc 1144 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   (φσ)    &   (((ψ χ θ) (τ η ζ) σ) → ρ)       (φρ)
 
Theoremsyl223anc 1145 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   (φσ)    &   (((ψ χ) (θ τ) (η ζ σ)) → ρ)       (φρ)
 
Theoremsyl232anc 1146 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   (φσ)    &   (((ψ χ) (θ τ η) (ζ σ)) → ρ)       (φρ)
 
Theoremsyl322anc 1147 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   (φσ)    &   (((ψ χ θ) (τ η) (ζ σ)) → ρ)       (φρ)
 
Theoremsyl233anc 1148 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   (φσ)    &   (φρ)    &   (((ψ χ) (θ τ η) (ζ σ ρ)) → μ)       (φμ)
 
Theoremsyl323anc 1149 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   (φσ)    &   (φρ)    &   (((ψ χ θ) (τ η) (ζ σ ρ)) → μ)       (φμ)
 
Theoremsyl332anc 1150 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   (φσ)    &   (φρ)    &   (((ψ χ θ) (τ η ζ) (σ ρ)) → μ)       (φμ)
 
Theoremsyl333anc 1151 A syllogism inference combined with contraction. (Contributed by NM, 10-Mar-2012.)
(φψ)    &   (φχ)    &   (φθ)    &   (φτ)    &   (φη)    &   (φζ)    &   (φσ)    &   (φρ)    &   (φμ)    &   (((ψ χ θ) (τ η ζ) (σ ρ μ)) → λ)       (φλ)
 
Theoremsyl3an1 1152 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
(φψ)    &   ((ψ χ θ) → τ)       ((φ χ θ) → τ)
 
Theoremsyl3an2 1153 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
(φχ)    &   ((ψ χ θ) → τ)       ((ψ φ θ) → τ)
 
Theoremsyl3an3 1154 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
(φθ)    &   ((ψ χ θ) → τ)       ((ψ χ φ) → τ)
 
Theoremsyl3an1b 1155 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
(φψ)    &   ((ψ χ θ) → τ)       ((φ χ θ) → τ)
 
Theoremsyl3an2b 1156 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
(φχ)    &   ((ψ χ θ) → τ)       ((ψ φ θ) → τ)
 
Theoremsyl3an3b 1157 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
(φθ)    &   ((ψ χ θ) → τ)       ((ψ χ φ) → τ)
 
Theoremsyl3an1br 1158 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
(ψφ)    &   ((ψ χ θ) → τ)       ((φ χ θ) → τ)
 
Theoremsyl3an2br 1159 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
(χφ)    &   ((ψ χ θ) → τ)       ((ψ φ θ) → τ)
 
Theoremsyl3an3br 1160 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
(θφ)    &   ((ψ χ θ) → τ)       ((ψ χ φ) → τ)
 
Theoremsyl3an 1161 A triple syllogism inference. (Contributed by NM, 13-May-2004.)
(φψ)    &   (χθ)    &   (τη)    &   ((ψ θ η) → ζ)       ((φ χ τ) → ζ)
 
Theoremsyl3anb 1162 A triple syllogism inference. (Contributed by NM, 15-Oct-2005.)
(φψ)    &   (χθ)    &   (τη)    &   ((ψ θ η) → ζ)       ((φ χ τ) → ζ)
 
Theoremsyl3anbr 1163 A triple syllogism inference. (Contributed by NM, 29-Dec-2011.)
(ψφ)    &   (θχ)    &   (ητ)    &   ((ψ θ η) → ζ)       ((φ χ τ) → ζ)
 
Theoremsyld3an3 1164 A syllogism inference. (Contributed by NM, 20-May-2007.)
((φ ψ χ) → θ)    &   ((φ ψ θ) → τ)       ((φ ψ χ) → τ)
 
Theoremsyld3an1 1165 A syllogism inference. (Contributed by NM, 7-Jul-2008.)
((χ ψ θ) → φ)    &   ((φ ψ θ) → τ)       ((χ ψ θ) → τ)
 
Theoremsyld3an2 1166 A syllogism inference. (Contributed by NM, 20-May-2007.)
((φ χ θ) → ψ)    &   ((φ ψ θ) → τ)       ((φ χ θ) → τ)
 
Theoremsyl3anl1 1167 A syllogism inference. (Contributed by NM, 24-Feb-2005.)
(φψ)    &   (((ψ χ θ) τ) → η)       (((φ χ θ) τ) → η)
 
Theoremsyl3anl2 1168 A syllogism inference. (Contributed by NM, 24-Feb-2005.)
(φχ)    &   (((ψ χ θ) τ) → η)       (((ψ φ θ) τ) → η)
 
Theoremsyl3anl3 1169 A syllogism inference. (Contributed by NM, 24-Feb-2005.)
(φθ)    &   (((ψ χ θ) τ) → η)       (((ψ χ φ) τ) → η)
 
Theoremsyl3anl 1170 A triple syllogism inference. (Contributed by NM, 24-Dec-2006.)
(φψ)    &   (χθ)    &   (τη)    &   (((ψ θ η) ζ) → σ)       (((φ χ τ) ζ) → σ)
 
Theoremsyl3anr1 1171 A syllogism inference. (Contributed by NM, 31-Jul-2007.)
(φψ)    &   ((χ (ψ θ τ)) → η)       ((χ (φ θ τ)) → η)
 
Theoremsyl3anr2 1172 A syllogism inference. (Contributed by NM, 1-Aug-2007.)
(φθ)    &   ((χ (ψ θ τ)) → η)       ((χ (ψ φ τ)) → η)
 
Theoremsyl3anr3 1173 A syllogism inference. (Contributed by NM, 23-Aug-2007.)
(φτ)    &   ((χ (ψ θ τ)) → η)       ((χ (ψ θ φ)) → η)
 
Theorem3impdi 1174 Importation inference (undistribute conjunction). (Contributed by NM, 14-Aug-1995.)
(((φ ψ) (φ χ)) → θ)       ((φ ψ χ) → θ)
 
Theorem3impdir 1175 Importation inference (undistribute conjunction). (Contributed by NM, 20-Aug-1995.)
(((φ ψ) (χ ψ)) → θ)       ((φ χ ψ) → θ)
 
Theorem3anidm12 1176 Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008.)
((φ φ ψ) → χ)       ((φ ψ) → χ)
 
Theorem3anidm13 1177 Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008.)
((φ ψ φ) → χ)       ((φ ψ) → χ)
 
Theorem3anidm23 1178 Inference from idempotent law for conjunction. (Contributed by NM, 1-Feb-2007.)
((φ ψ ψ) → χ)       ((φ ψ) → χ)
 
Theorem3ori 1179 Infer implication from triple disjunction. (Contributed by NM, 26-Sep-2006.)
(φ ψ χ)       ((¬ φ ¬ ψ) → χ)
 
Theorem3jao 1180 Disjunction of 3 antecedents. (Contributed by NM, 8-Apr-1994.)
(((φψ) (χψ) (θψ)) → ((φ χ θ) → ψ))
 
Theorem3jaob 1181 Disjunction of 3 antecedents. (Contributed by NM, 13-Sep-2011.)
(((φ χ θ) → ψ) ↔ ((φψ) (χψ) (θψ)))
 
Theorem3jaoi 1182 Disjunction of 3 antecedents (inference). (Contributed by NM, 12-Sep-1995.)
(φψ)    &   (χψ)    &   (θψ)       ((φ χ θ) → ψ)
 
Theorem3jaod 1183 Disjunction of 3 antecedents (deduction). (Contributed by NM, 14-Oct-2005.)
(φ → (ψχ))    &   (φ → (θχ))    &   (φ → (τχ))       (φ → ((ψ θ τ) → χ))
 
Theorem3jaoian 1184 Disjunction of 3 antecedents (inference). (Contributed by NM, 14-Oct-2005.)
((φ ψ) → χ)    &   ((θ ψ) → χ)    &   ((τ ψ) → χ)       (((φ θ τ) ψ) → χ)
 
Theorem3jaodan 1185 Disjunction of 3 antecedents (deduction). (Contributed by NM, 14-Oct-2005.)
((φ ψ) → χ)    &   ((φ θ) → χ)    &   ((φ τ) → χ)       ((φ (ψ θ τ)) → χ)
 
Theorem3jaao 1186 Inference conjoining and disjoining the antecedents of three implications. (Contributed by Jeff Hankins, 15-Aug-2009.) (Proof shortened by Andrew Salmon, 13-May-2011.)
(φ → (ψχ))    &   (θ → (τχ))    &   (η → (ζχ))       ((φ θ η) → ((ψ τ ζ) → χ))
 
Theorem3ianorr 1187 Triple disjunction implies negated triple conjunction. (Contributed by Jim Kingdon, 23-Dec-2018.)
((¬ φ ¬ ψ ¬ χ) → ¬ (φ ψ χ))
 
Theoremsyl3an9b 1188 Nested syllogism inference conjoining 3 dissimilar antecedents. (Contributed by NM, 1-May-1995.)
(φ → (ψχ))    &   (θ → (χτ))    &   (η → (τζ))       ((φ θ η) → (ψζ))
 
Theorem3orbi123d 1189 Deduction joining 3 equivalences to form equivalence of disjunctions. (Contributed by NM, 20-Apr-1994.)
(φ → (ψχ))    &   (φ → (θτ))    &   (φ → (ηζ))       (φ → ((ψ θ η) ↔ (χ τ ζ)))
 
Theorem3anbi123d 1190 Deduction joining 3 equivalences to form equivalence of conjunctions. (Contributed by NM, 22-Apr-1994.)
(φ → (ψχ))    &   (φ → (θτ))    &   (φ → (ηζ))       (φ → ((ψ θ η) ↔ (χ τ ζ)))
 
Theorem3anbi12d 1191 Deduction conjoining and adding a conjunct to equivalences. (Contributed by NM, 8-Sep-2006.)
(φ → (ψχ))    &   (φ → (θτ))       (φ → ((ψ θ η) ↔ (χ τ η)))
 
Theorem3anbi13d 1192 Deduction conjoining and adding a conjunct to equivalences. (Contributed by NM, 8-Sep-2006.)
(φ → (ψχ))    &   (φ → (θτ))       (φ → ((ψ η θ) ↔ (χ η τ)))
 
Theorem3anbi23d 1193 Deduction conjoining and adding a conjunct to equivalences. (Contributed by NM, 8-Sep-2006.)
(φ → (ψχ))    &   (φ → (θτ))       (φ → ((η ψ θ) ↔ (η χ τ)))
 
Theorem3anbi1d 1194 Deduction adding conjuncts to an equivalence. (Contributed by NM, 8-Sep-2006.)
(φ → (ψχ))       (φ → ((ψ θ τ) ↔ (χ θ τ)))
 
Theorem3anbi2d 1195 Deduction adding conjuncts to an equivalence. (Contributed by NM, 8-Sep-2006.)
(φ → (ψχ))       (φ → ((θ ψ τ) ↔ (θ χ τ)))
 
Theorem3anbi3d 1196 Deduction adding conjuncts to an equivalence. (Contributed by NM, 8-Sep-2006.)
(φ → (ψχ))       (φ → ((θ τ ψ) ↔ (θ τ χ)))
 
Theorem3anim123d 1197 Deduction joining 3 implications to form implication of conjunctions. (Contributed by NM, 24-Feb-2005.)
(φ → (ψχ))    &   (φ → (θτ))    &   (φ → (ηζ))       (φ → ((ψ θ η) → (χ τ ζ)))
 
Theorem3orim123d 1198 Deduction joining 3 implications to form implication of disjunctions. (Contributed by NM, 4-Apr-1997.)
(φ → (ψχ))    &   (φ → (θτ))    &   (φ → (ηζ))       (φ → ((ψ θ η) → (χ τ ζ)))
 
Theoreman6 1199 Rearrangement of 6 conjuncts. (Contributed by NM, 13-Mar-1995.)
(((φ ψ χ) (θ τ η)) ↔ ((φ θ) (ψ τ) (χ η)))
 
Theorem3an6 1200 Analog of an4 507 for triple conjunction. (Contributed by Scott Fenton, 16-Mar-2011.) (Proof shortened by Andrew Salmon, 25-May-2011.)
(((φ ψ) (χ θ) (τ η)) ↔ ((φ χ τ) (ψ θ η)))
    < Previous  Next >

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 7401-7411
  Copyright terms: Public domain < Previous  Next >