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Theorem anidmdbi 627
Description: Conjunction idempotence with antecedent. (Contributed by Roy F. Longton, 8-Aug-2005.)
Assertion
Ref Expression
anidmdbi  |-  ( (
ph  ->  ( ps  /\  ps ) )  <->  ( ph  ->  ps ) )

Proof of Theorem anidmdbi
StepHypRef Expression
1 anidm 625 . 2  |-  ( ( ps  /\  ps )  <->  ps )
21imbi2i 303 1  |-  ( (
ph  ->  ( ps  /\  ps ) )  <->  ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  nanim  1292  inposet  25278  1ded  25738
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
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