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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 ((ψ φ) ↔ (χ φ))

Proof of Theorem pm5.32ri
StepHypRef Expression
1 pm5.32i.1 . . 3 (φ → (ψχ))
21pm5.32i 427 . 2 ((φ ψ) ↔ (φ χ))
3 ancom 253 . 2 ((ψ φ) ↔ (φ ψ))
4 ancom 253 . 2 ((χ φ) ↔ (φ χ))
52, 3, 43bitr4i 201 1 ((ψ φ) ↔ (χ φ))
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  707  oranabs  727  ceqsralt  2575  ceqsrexbv  2669  reuind  2738  rabsn  3428  dfoprab2  5494  xpsnen  6231  nn1suc  7714
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