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Theorem anidmdbi 384
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 382 . 2 ((𝜓𝜓) ↔ 𝜓)
21imbi2i 219 1 ((𝜑 → (𝜓𝜓)) ↔ (𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by: (None)
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