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Theorem pm5.3 459
Description: Theorem *5.3 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Andrew Salmon, 7-May-2011.)
Assertion
Ref Expression
pm5.3  |-  ( ( ( ph  /\  ps )  ->  ch )  <->  ( ( ph  /\  ps )  -> 
( ph  /\  ch )
) )

Proof of Theorem pm5.3
StepHypRef Expression
1 impexp 259 . 2  |-  ( ( ( ph  /\  ps )  ->  ch )  <->  ( ph  ->  ( ps  ->  ch ) ) )
2 imdistan 433 . 2  |-  ( (
ph  ->  ( ps  ->  ch ) )  <->  ( ( ph  /\  ps )  -> 
( ph  /\  ch )
) )
31, 2bitri 182 1  |-  ( ( ( ph  /\  ps )  ->  ch )  <->  ( ( ph  /\  ps )  -> 
( ph  /\  ch )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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