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Theorem pm4.71d 379
Description: Deduction converting an implication to a biconditional with conjunction. Deduction from Theorem *4.71 of [WhiteheadRussell] p. 120. (Contributed by Mario Carneiro, 25-Dec-2016.)
Hypothesis
Ref Expression
pm4.71rd.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
pm4.71d (𝜑 → (𝜓 ↔ (𝜓𝜒)))

Proof of Theorem pm4.71d
StepHypRef Expression
1 pm4.71rd.1 . 2 (𝜑 → (𝜓𝜒))
2 pm4.71 375 . 2 ((𝜓𝜒) ↔ (𝜓 ↔ (𝜓𝜒)))
31, 2sylib 131 1 (𝜑 → (𝜓 ↔ (𝜓𝜒)))
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:  difin2  3227  resopab2  4683  fcnvres  5101  resoprab2  5626
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