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Theorem anabs1 783
Description: Absorption into embedded conjunct. (Contributed by NM, 4-Sep-1995.) (Proof shortened by Wolf Lammen, 16-Nov-2013.)
Assertion
Ref Expression
anabs1  |-  ( ( ( ph  /\  ps )  /\  ph )  <->  ( ph  /\ 
ps ) )

Proof of Theorem anabs1
StepHypRef Expression
1 simpl 443 . . 3  |-  ( (
ph  /\  ps )  ->  ph )
21pm4.71i 613 . 2  |-  ( (
ph  /\  ps )  <->  ( ( ph  /\  ps )  /\  ph ) )
32bicomi 193 1  |-  ( ( ( ph  /\  ps )  /\  ph )  <->  ( ph  /\ 
ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358
This theorem is referenced by:  poirr  4325  mndcl  14372  frgra3v  28180  uun121p1  28559
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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