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Theorem syl7 63
Description: A syllogism rule of inference. The second premise is used to replace the third antecedent of the first premise. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 3-Aug-2012.)
Hypotheses
Ref Expression
syl7.1 (φψ)
syl7.2 (χ → (θ → (ψτ)))
Assertion
Ref Expression
syl7 (χ → (θ → (φτ)))

Proof of Theorem syl7
StepHypRef Expression
1 syl7.1 . . 3 (φψ)
21a1i 9 . 2 (χ → (φψ))
3 syl7.2 . 2 (χ → (θ → (ψτ)))
42, 3syl5d 62 1 (χ → (θ → (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:  syl7bi  154  syl3an3  1169  fvmptt  5205
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