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Theorem pm4.71d 391
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 pm4.71 387 . 2 ((𝜓𝜒) ↔ (𝜓 ↔ (𝜓𝜒)))
31, 2sylib 121 1 (𝜑 → (𝜓 ↔ (𝜓𝜒)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  difin2  3342  resopab2  4873  fcnvres  5313  resoprab2  5875  cndis  12447  cnpdis  12448  blpnf  12606
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