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Theorem pm5.74d 175
Description: Distribution of implication over biconditional (deduction rule). (Contributed by NM, 21-Mar-1996.)
Hypothesis
Ref Expression
pm5.74d.1 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
pm5.74d (𝜑 → ((𝜓𝜒) ↔ (𝜓𝜃)))

Proof of Theorem pm5.74d
StepHypRef Expression
1 pm5.74d.1 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
2 pm5.74 172 . 2 ((𝜓 → (𝜒𝜃)) ↔ ((𝜓𝜒) ↔ (𝜓𝜃)))
31, 2sylib 131 1 (𝜑 → ((𝜓𝜒) ↔ (𝜓𝜃)))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  imbi2d  223  imim21b  245  pm5.74da  425  cbval2  1812  dfiin2g  3718  brecop  6227  dom2lem  6283  nn0ind-raph  8414
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