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Theorem syl6ci 1331
Description: A syllogism inference combined with contraction. (Contributed by Alan Sare, 18-Mar-2012.)
Hypotheses
Ref Expression
syl6ci.1 (φ → (ψχ))
syl6ci.2 (φθ)
syl6ci.3 (χ → (θτ))
Assertion
Ref Expression
syl6ci (φ → (ψτ))

Proof of Theorem syl6ci
StepHypRef Expression
1 syl6ci.1 . 2 (φ → (ψχ))
2 syl6ci.2 . . 3 (φθ)
32a1d 22 . 2 (φ → (ψθ))
4 syl6ci.3 . 2 (χ → (θτ))
51, 3, 4syl6c 60 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:  ltxrlt  6842  ltnsym  6861
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