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Theorem pm2.86d 93
Description: Deduction based on pm2.86 94. (Contributed by NM, 29-Jun-1995.) (Proof shortened by Wolf Lammen, 3-Apr-2013.)
Hypothesis
Ref Expression
pm2.86d.1 (φ → ((ψχ) → (ψθ)))
Assertion
Ref Expression
pm2.86d (φ → (ψ → (χθ)))

Proof of Theorem pm2.86d
StepHypRef Expression
1 ax-1 6 . . 3 (χ → (ψχ))
2 pm2.86d.1 . . 3 (φ → ((ψχ) → (ψθ)))
31, 2syl5 28 . 2 (φ → (χ → (ψθ)))
43com23 72 1 (φ → (ψ → (χθ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  pm2.86  94  pm5.74  235  ax12olem6  1932  ax15  2021
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