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Theorem pm5.74rd 266
Description: Distribution of implication over biconditional (deduction form). (Contributed by NM, 19-Mar-1997.)
Hypothesis
Ref Expression
pm5.74rd.1 (𝜑 → ((𝜓𝜒) ↔ (𝜓𝜃)))
Assertion
Ref Expression
pm5.74rd (𝜑 → (𝜓 → (𝜒𝜃)))

Proof of Theorem pm5.74rd
StepHypRef Expression
1 pm5.74rd.1 . 2 (𝜑 → ((𝜓𝜒) ↔ (𝜓𝜃)))
2 pm5.74 262 . 2 ((𝜓 → (𝜒𝜃)) ↔ ((𝜓𝜒) ↔ (𝜓𝜃)))
31, 2sylibr 226 1 (𝜑 → (𝜓 → (𝜒𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 198
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 199
This theorem is referenced by:  pm5.35  857  wl-dral1d  33801
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