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Theorem anabs1 561
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 108 . . 3  |-  ( (
ph  /\  ps )  ->  ph )
21pm4.71i 388 . 2  |-  ( (
ph  /\  ps )  <->  ( ( ph  /\  ps )  /\  ph ) )
32bicomi 131 1  |-  ( ( ( ph  /\  ps )  /\  ph )  <->  ( ph  /\ 
ps ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  poirr  4224
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