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Theorem pm5.74d 182
Description: Distribution of implication over biconditional (deduction form). (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 pm5.74 179 . 2 ((𝜓 → (𝜒𝜃)) ↔ ((𝜓𝜒) ↔ (𝜓𝜃)))
31, 2sylib 122 1 (𝜑 → ((𝜓𝜒) ↔ (𝜓𝜃)))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  imbi2d  230  imim21b  253  pm5.74da  443  cbval2  1919  dfiin2g  3915  brecop  6615  dom2lem  6762  nn0ind-raph  9341
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