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Theorem anabs5 807
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 504 . . 3  |-  ( ph  ->  ( ps  <->  ( ph  /\ 
ps ) ) )
21bicomd 201 . 2  |-  ( ph  ->  ( ( ph  /\  ps )  <->  ps ) )
32pm5.32i 637 1  |-  ( (
ph  /\  ( ph  /\ 
ps ) )  <->  ( ph  /\ 
ps ) )
Colors of variables: wff setvar class
Syntax hints:    <-> 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:  axrep5  4568  axsep2  4574  2sb5nd  32706  eelTT1  32875  uun121  32953  uunTT1  32963  uunTT1p1  32964  uunTT1p2  32965  uun111  32975  uun2221  32983  uun2221p1  32984  uun2221p2  32985  2sb5ndVD  33083  2sb5ndALT  33105  bj-axrep5  33752
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