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Theorem syl313anc 1208
 Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
Hypotheses
Ref Expression
sylXanc.1
sylXanc.2
sylXanc.3
sylXanc.4
sylXanc.5
sylXanc.6
sylXanc.7
syl313anc.8
Assertion
Ref Expression
syl313anc

Proof of Theorem syl313anc
StepHypRef Expression
1 sylXanc.1 . 2
2 sylXanc.2 . 2
3 sylXanc.3 . 2
4 sylXanc.4 . 2
5 sylXanc.5 . . 3
6 sylXanc.6 . . 3
7 sylXanc.7 . . 3
85, 6, 73jca 1134 . 2
9 syl313anc.8 . 2
101, 2, 3, 4, 8, 9syl311anc 1198 1
 Colors of variables: wff set class Syntax hints:   wi 4   w3a 936 This theorem is referenced by:  syl323anc  1214  osumcllem6N  30695  cdlemg13  31386  cdlemk7u  31604  cdlemk31  31630  cdlemk27-3  31641  cdlemk19ylem  31664  cdlemk46  31682 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 178  df-an 361  df-3an 938
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