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Theorem syl13anc 1184
Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
Hypotheses
Ref Expression
sylXanc.1
sylXanc.2
sylXanc.3
sylXanc.4
syl13anc.5
Assertion
Ref Expression
syl13anc

Proof of Theorem syl13anc
StepHypRef Expression
1 sylXanc.1 . 2
2 sylXanc.2 . . 3
3 sylXanc.3 . . 3
4 sylXanc.4 . . 3
52, 3, 43jca 1132 . 2
6 syl13anc.5 . 2
71, 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:  syl23anc  1189  syl33anc  1197  pm2.61da3ne  2596  sbthlem3  6205
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