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Theorem oranabs 762
Description: Absorb a disjunct into a conjunct. (Contributed by Roy F. Longton, 23-Jun-2005.) (Proof shortened by Wolf Lammen, 10-Nov-2013.)
Assertion
Ref Expression
oranabs  |-  ( ( ( ph  \/  -.  ps )  /\  ps )  <->  (
ph  /\  ps )
)

Proof of Theorem oranabs
StepHypRef Expression
1 biortn 697 . . 3  |-  ( ps 
->  ( ph  <->  ( -.  ps  \/  ph ) ) )
2 orcom 680 . . 3  |-  ( ( -.  ps  \/  ph ) 
<->  ( ph  \/  -.  ps ) )
31, 2syl6rbb 195 . 2  |-  ( ps 
->  ( ( ph  \/  -.  ps )  <->  ph ) )
43pm5.32ri 443 1  |-  ( ( ( ph  \/  -.  ps )  /\  ps )  <->  (
ph  /\  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 102    <-> wb 103    \/ wo 662
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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