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Theorem syl3c 57
Description: A syllogism inference combined with contraction. (Contributed by Alan Sare, 7-Jul-2011.)
Hypotheses
Ref Expression
syl3c.1 (φψ)
syl3c.2 (φχ)
syl3c.3 (φθ)
syl3c.4 (ψ → (χ → (θτ)))
Assertion
Ref Expression
syl3c (φτ)

Proof of Theorem syl3c
StepHypRef Expression
1 syl3c.3 . 2 (φθ)
2 syl3c.1 . . 3 (φψ)
3 syl3c.2 . . 3 (φχ)
4 syl3c.4 . . 3 (ψ → (χ → (θτ)))
52, 3, 4sylc 56 . 2 (φ → (θτ))
61, 5mpd 13 1 (φτ)
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  bilukdc  1284  tfrlem1  5864  peano5uzti  8082
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