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Theorem syl6c 60
Description: Inference combining syl6 29 with contraction. (Contributed by Alan Sare, 2-May-2011.)
Hypotheses
Ref Expression
syl6c.1 (φ → (ψχ))
syl6c.2 (φ → (ψθ))
syl6c.3 (χ → (θτ))
Assertion
Ref Expression
syl6c (φ → (ψτ))

Proof of Theorem syl6c
StepHypRef Expression
1 syl6c.2 . 2 (φ → (ψθ))
2 syl6c.1 . . 3 (φ → (ψχ))
3 syl6c.3 . . 3 (χ → (θτ))
42, 3syl6 29 . 2 (φ → (ψ → (θτ)))
51, 4mpdd 36 1 (φ → (ψτ))
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:  syldd  61  impbidd  118  jcad  291  dcbi  843  pm3.13dc  865  syl6ci  1331
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