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Theorem pm5.32ri 619
 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 618 . 2 ((φ ψ) ↔ (φ χ))
3 ancom 437 . 2 ((ψ φ) ↔ (φ ψ))
4 ancom 437 . 2 ((χ φ) ↔ (φ χ))
52, 3, 43bitr4i 268 1 ((ψ φ) ↔ (χ φ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-an 360 This theorem is referenced by:  anbi1i  676  pm5.61  693  oranabs  829  pm5.36  849  2eu5  2288  ceqsralt  2882  ceqsrexbv  2973  reuind  3039  rabsn  3790  elpw1  4144  pw1in  4164  addccan2nclem1  6263  scancan  6331
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