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Theorem syl131anc 1195
Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
Hypotheses
Ref Expression
sylXanc.1
sylXanc.2
sylXanc.3
sylXanc.4
sylXanc.5
syl131anc.6
Assertion
Ref Expression
syl131anc

Proof of Theorem syl131anc
StepHypRef Expression
1 sylXanc.1 . 2
2 sylXanc.2 . . 3
3 sylXanc.3 . . 3
4 sylXanc.4 . . 3
52, 3, 43jca 1132 . 2
6 sylXanc.5 . 2
7 syl131anc.6 . 2
81, 5, 6, 7syl3anc 1182 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   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:  syl132anc  1200  syl231anc  1202  syl133anc  1205
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