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Theorem syl12anc 1180
Description: Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009.)
Hypotheses
Ref Expression
sylXanc.1
sylXanc.2
sylXanc.3
syl12anc.4
Assertion
Ref Expression
syl12anc

Proof of Theorem syl12anc
StepHypRef Expression
1 sylXanc.1 . . 3
2 sylXanc.2 . . 3
3 sylXanc.3 . . 3
41, 2, 3jca32 521 . 2
5 syl12anc.4 . 2
64, 5syl 15 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wa 358
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 177  df-an 360
This theorem is referenced by:  syl22anc  1183  raaan  3657  raaanv  3658  nndisjeq  4429  prepeano4  4451  ssfin  4470  ncfinraise  4481  ncfinlower  4483  nnpweq  4523  peano4  4557  f1oiso2  5500  frecsuc  6322
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