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Theorem pm4.44 563
Description: Theorem *4.44 of [WhiteheadRussell] p. 119. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.44  |-  ( ph  <->  (
ph  \/  ( ph  /\ 
ps ) ) )

Proof of Theorem pm4.44
StepHypRef Expression
1 orc 376 . 2  |-  ( ph  ->  ( ph  \/  ( ph  /\  ps ) ) )
2 id 21 . . 3  |-  ( ph  ->  ph )
3 simpl 445 . . 3  |-  ( (
ph  /\  ps )  ->  ph )
42, 3jaoi 370 . 2  |-  ( (
ph  \/  ( ph  /\ 
ps ) )  ->  ph )
51, 4impbii 182 1  |-  ( ph  <->  (
ph  \/  ( ph  /\ 
ps ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    \/ wo 359    /\ wa 360
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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