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Theorem syl31anc 1185
Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
Hypotheses
Ref Expression
sylXanc.1
sylXanc.2
sylXanc.3
sylXanc.4
syl31anc.5
Assertion
Ref Expression
syl31anc

Proof of Theorem syl31anc
StepHypRef Expression
1 sylXanc.1 . . 3
2 sylXanc.2 . . 3
3 sylXanc.3 . . 3
41, 2, 33jca 1132 . 2
5 sylXanc.4 . 2
6 syl31anc.5 . 2
74, 5, 6syl2anc 642 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wa 358   w3a 934
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
This theorem is referenced by:  syl32anc  1190  ltfinirr  4457  vfin1cltv  4547  leconnnc  6218  tlecg  6230
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