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Theorem syl12anc 1180
 Description: Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009.)
Hypotheses
Ref Expression
sylXanc.1 (φψ)
sylXanc.2 (φχ)
sylXanc.3 (φθ)
syl12anc.4 ((ψ (χ θ)) → τ)
Assertion
Ref Expression
syl12anc (φτ)

Proof of Theorem syl12anc
StepHypRef Expression
1 sylXanc.1 . . 3 (φψ)
2 sylXanc.2 . . 3 (φχ)
3 sylXanc.3 . . 3 (φθ)
41, 2, 3jca32 521 . 2 (φ → (ψ (χ θ)))
5 syl12anc.4 . 2 ((ψ (χ θ)) → τ)
64, 5syl 15 1 (φτ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358 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 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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