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Theorem anabs5 816
Description: Absorption into embedded conjunct. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 9-Dec-2012.)
Assertion
Ref Expression
anabs5  |-  ( (
ph  /\  ( ph  /\ 
ps ) )  <->  ( ph  /\ 
ps ) )

Proof of Theorem anabs5
StepHypRef Expression
1 ibar 506 . . 3  |-  ( ph  ->  ( ps  <->  ( ph  /\ 
ps ) ) )
21bicomd 204 . 2  |-  ( ph  ->  ( ( ph  /\  ps )  <->  ps ) )
32pm5.32i 641 1  |-  ( (
ph  /\  ( ph  /\ 
ps ) )  <->  ( ph  /\ 
ps ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 187    /\ wa 370
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 188  df-an 372
This theorem is referenced by:  axrep5  4543  axsep2  4549  bj-axrep5  31166  2sb5nd  36579  eelTT1  36748  uun121  36825  uunTT1  36835  uunTT1p1  36836  uunTT1p2  36837  uun111  36847  uun2221  36855  uun2221p1  36856  uun2221p2  36857  2sb5ndVD  36962  2sb5ndALT  36984
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