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Theorem pm5.32ri 450
 Description: Distribution of implication over biconditional (inference form). (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 449 . 2 ((𝜑𝜓) ↔ (𝜑𝜒))
3 ancom 264 . 2 ((𝜓𝜑) ↔ (𝜑𝜓))
4 ancom 264 . 2 ((𝜒𝜑) ↔ (𝜑𝜒))
52, 3, 43bitr4i 211 1 ((𝜓𝜑) ↔ (𝜒𝜑))
 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:  anbi1i  453  pm5.36  599  pm5.61  783  oranabs  804  ceqsralt  2713  ceqsrexbv  2816  reuind  2889  rabsn  3590  dfoprab2  5818  xpsnen  6715  nn1suc  8739  isprm2  11798  isxms2  12621
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