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Theorem pm2.86d 97
Description: Deduction based on pm2.86 98. (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 5 . . 3 (𝜒 → (𝜓𝜒))
2 pm2.86d.1 . . 3 (𝜑 → ((𝜓𝜒) → (𝜓𝜃)))
31, 2syl5 32 . 2 (𝜑 → (𝜒 → (𝜓𝜃)))
43com23 76 1 (𝜑 → (𝜓 → (𝜒𝜃)))
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:  pm2.86  98  pm5.74  172
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