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Theorem pm5.32rd 424
Description: Distribution of implication over biconditional (deduction rule). (Contributed by NM, 25-Dec-2004.)
Hypothesis
Ref Expression
pm5.32d.1 (φ → (ψ → (χθ)))
Assertion
Ref Expression
pm5.32rd (φ → ((χ ψ) ↔ (θ ψ)))

Proof of Theorem pm5.32rd
StepHypRef Expression
1 pm5.32d.1 . . 3 (φ → (ψ → (χθ)))
21pm5.32d 423 . 2 (φ → ((ψ χ) ↔ (ψ θ)))
3 ancom 253 . 2 ((χ ψ) ↔ (ψ χ))
4 ancom 253 . 2 ((θ ψ) ↔ (ψ θ))
52, 3, 43bitr4g 212 1 (φ → ((χ ψ) ↔ (θ ψ)))
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:  anbi1d  438  pm5.71dc  867  1idprl  6565  1idpru  6566
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