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Theorem pm4.42 931
Description: Theorem *4.42 of [WhiteheadRussell] p. 119. (Contributed by Roy F. Longton, 21-Jun-2005.)
Assertion
Ref Expression
pm4.42  |-  ( ph  <->  ( ( ph  /\  ps )  \/  ( ph  /\ 
-.  ps ) ) )

Proof of Theorem pm4.42
StepHypRef Expression
1 dedlema 925 . 2  |-  ( ps 
->  ( ph  <->  ( ( ph  /\  ps )  \/  ( ph  /\  -.  ps ) ) ) )
2 dedlemb 926 . 2  |-  ( -. 
ps  ->  ( ph  <->  ( ( ph  /\  ps )  \/  ( ph  /\  -.  ps ) ) ) )
31, 2pm2.61i 158 1  |-  ( ph  <->  ( ( ph  /\  ps )  \/  ( ph  /\ 
-.  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    <-> wb 178    \/ wo 359    /\ wa 360
This theorem is referenced by:  inundif  3533  expdioph  26515
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362
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