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Theorem anidmdbi 627
Description: Conjunction idempotence with antecedent. (Contributed by Roy F. Longton, 8-Aug-2005.)
Assertion
Ref Expression
anidmdbi ((φ → (ψ ψ)) ↔ (φψ))

Proof of Theorem anidmdbi
StepHypRef Expression
1 anidm 625 . 2 ((ψ ψ) ↔ ψ)
21imbi2i 303 1 ((φ → (ψ ψ)) ↔ (φψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wa 358
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360
This theorem is referenced by:  nanim  1292
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