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Theorem syl5d 62
Description: A nested syllogism deduction. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.) (Proof shortened by O'Cat, 2-Feb-2006.)
Hypotheses
Ref Expression
syl5d.1 (φ → (ψχ))
syl5d.2 (φ → (θ → (χτ)))
Assertion
Ref Expression
syl5d (φ → (θ → (ψτ)))

Proof of Theorem syl5d
StepHypRef Expression
1 syl5d.1 . . 3 (φ → (ψχ))
21a1d 22 . 2 (φ → (θ → (ψχ)))
3 syl5d.2 . 2 (φ → (θ → (χτ)))
42, 3syldd 61 1 (φ → (θ → (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:  syl7  63  syl9  66  imim12d  68  jaddc  760  pm4.79dc  808
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