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Theorem pm4.71d 373
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 ↔ (ψ χ)))

Proof of Theorem pm4.71d
StepHypRef Expression
1 pm4.71rd.1 . 2 (φ → (ψχ))
2 pm4.71 369 . 2 ((ψχ) ↔ (ψ ↔ (ψ χ)))
31, 2sylib 127 1 (φ → (ψ ↔ (ψ χ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  difin2  3193  resopab2  4598  fcnvres  5016  resoprab2  5540
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