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Theorem syl21anc 1181
Description: Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009.)
Hypotheses
Ref Expression
sylXanc.1 (φψ)
sylXanc.2 (φχ)
sylXanc.3 (φθ)
syl21anc.4 (((ψ χ) θ) → τ)
Assertion
Ref Expression
syl21anc (φτ)

Proof of Theorem syl21anc
StepHypRef Expression
1 sylXanc.1 . . 3 (φψ)
2 sylXanc.2 . . 3 (φχ)
3 sylXanc.3 . . 3 (φθ)
41, 2, 3jca31 520 . 2 (φ → ((ψ χ) θ))
5 syl21anc.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:  funprgOLD  5150  fnunsn  5190  fvun1  5379
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