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Theorem pm5.74da 425
Description: Distribution of implication over biconditional (deduction rule). (Contributed by NM, 4-May-2007.)
Hypothesis
Ref Expression
pm5.74da.1 ((𝜑𝜓) → (𝜒𝜃))
Assertion
Ref Expression
pm5.74da (𝜑 → ((𝜓𝜒) ↔ (𝜓𝜃)))

Proof of Theorem pm5.74da
StepHypRef Expression
1 pm5.74da.1 . . 3 ((𝜑𝜓) → (𝜒𝜃))
21ex 112 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
32pm5.74d 175 1 (𝜑 → ((𝜓𝜒) ↔ (𝜓𝜃)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  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:  ralbida  2337  elrab3t  2720  dff13  5435
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