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Theorem pm5.42 533
Description: Theorem *5.42 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.42  |-  ( (
ph  ->  ( ps  ->  ch ) )  <->  ( ph  ->  ( ps  ->  ( ph  /\  ch ) ) ) )

Proof of Theorem pm5.42
StepHypRef Expression
1 ibar 492 . . 3  |-  ( ph  ->  ( ch  <->  ( ph  /\ 
ch ) ) )
21imbi2d 309 . 2  |-  ( ph  ->  ( ( ps  ->  ch )  <->  ( ps  ->  (
ph  /\  ch )
) ) )
32pm5.74i 238 1  |-  ( (
ph  ->  ( ps  ->  ch ) )  <->  ( ph  ->  ( ps  ->  ( ph  /\  ch ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178    /\ wa 360
This theorem is referenced by:  anc2l  540  imdistan  673
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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