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Theorem anidmdbi 677
Description: Conjunction idempotence with antecedent. (Contributed by Roy F. Longton, 8-Aug-2005.)
Assertion
Ref Expression
anidmdbi ((𝜑 → (𝜓𝜓)) ↔ (𝜑𝜓))

Proof of Theorem anidmdbi
StepHypRef Expression
1 anidm 675 . 2 ((𝜓𝜓) ↔ 𝜓)
21imbi2i 326 1 ((𝜑 → (𝜓𝜓)) ↔ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 384
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 197  df-an 386
This theorem is referenced by:  nanim  1449
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