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Theorem pm5.33 853
Description: Theorem *5.33 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.33  |-  ( (
ph  /\  ( ps  ->  ch ) )  <->  ( ph  /\  ( ( ph  /\  ps )  ->  ch )
) )

Proof of Theorem pm5.33
StepHypRef Expression
1 ibar 492 . . 3  |-  ( ph  ->  ( ps  <->  ( ph  /\ 
ps ) ) )
21imbi1d 310 . 2  |-  ( ph  ->  ( ( ps  ->  ch )  <->  ( ( ph  /\ 
ps )  ->  ch ) ) )
32pm5.32i 621 1  |-  ( (
ph  /\  ( ps  ->  ch ) )  <->  ( ph  /\  ( ( ph  /\  ps )  ->  ch )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178    /\ 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-an 362
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