MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  anidmdbi Structured version   Unicode version

Theorem anidmdbi 646
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 644 . 2  |-  ( ( ps  /\  ps )  <->  ps )
21imbi2i 312 1  |-  ( (
ph  ->  ( ps  /\  ps ) )  <->  ( ph  ->  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ wa 369
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 185  df-an 371
This theorem is referenced by:  nanim  1338
  Copyright terms: Public domain W3C validator