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Theorem syl6d 64
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.) (Revised by NM, 3-Feb-2006.)
Hypotheses
Ref Expression
syl6d.1 (φ → (ψ → (χθ)))
syl6d.2 (φ → (θτ))
Assertion
Ref Expression
syl6d (φ → (ψ → (χτ)))

Proof of Theorem syl6d
StepHypRef Expression
1 syl6d.1 . 2 (φ → (ψ → (χθ)))
2 syl6d.2 . . 3 (φ → (θτ))
32a1d 22 . 2 (φ → (ψ → (θτ)))
41, 3syldd 61 1 (φ → (ψ → (χτ)))
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:  syl8  65
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