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Theorem pm4.44 560
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 374 . 2  |-  ( ph  ->  ( ph  \/  ( ph  /\  ps ) ) )
2 id 19 . . 3  |-  ( ph  ->  ph )
3 simpl 443 . . 3  |-  ( (
ph  /\  ps )  ->  ph )
42, 3jaoi 368 . 2  |-  ( (
ph  \/  ( ph  /\ 
ps ) )  ->  ph )
51, 4impbii 180 1  |-  ( ph  <->  (
ph  \/  ( ph  /\ 
ps ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    \/ wo 357    /\ wa 358
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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