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Theorem pm4.42 926
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 920 . 2  |-  ( ps 
->  ( ph  <->  ( ( ph  /\  ps )  \/  ( ph  /\  -.  ps ) ) ) )
2 dedlemb 921 . 2  |-  ( -. 
ps  ->  ( ph  <->  ( ( ph  /\  ps )  \/  ( ph  /\  -.  ps ) ) ) )
31, 2pm2.61i 156 1  |-  ( ph  <->  ( ( ph  /\  ps )  \/  ( ph  /\ 
-.  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    \/ wo 357    /\ wa 358
This theorem is referenced by:  inundif  3532  elim2ifim  23153  expdioph  27116
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-or 359  df-an 360
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