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Theorem pm5.32ri 428
 Description: Distribution of implication over biconditional (inference rule). (Contributed by NM, 12-Mar-1995.)
Hypothesis
Ref Expression
pm5.32i.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
pm5.32ri ((𝜓𝜑) ↔ (𝜒𝜑))

Proof of Theorem pm5.32ri
StepHypRef Expression
1 pm5.32i.1 . . 3 (𝜑 → (𝜓𝜒))
21pm5.32i 427 . 2 ((𝜑𝜓) ↔ (𝜑𝜒))
3 ancom 253 . 2 ((𝜓𝜑) ↔ (𝜑𝜓))
4 ancom 253 . 2 ((𝜒𝜑) ↔ (𝜑𝜒))
52, 3, 43bitr4i 201 1 ((𝜓𝜑) ↔ (𝜒𝜑))
 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:  anbi1i  431  pm5.36  542  pm5.61  708  oranabs  728  ceqsralt  2581  ceqsrexbv  2675  reuind  2744  rabsn  3437  dfoprab2  5552  xpsnen  6295  nn1suc  7933
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