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Theorem imdistan 433
Description: Distribution of implication with conjunction. (Contributed by NM, 31-May-1999.) (Proof shortened by Wolf Lammen, 6-Dec-2012.)
Assertion
Ref Expression
imdistan  |-  ( (
ph  ->  ( ps  ->  ch ) )  <->  ( ( ph  /\  ps )  -> 
( ph  /\  ch )
) )

Proof of Theorem imdistan
StepHypRef Expression
1 pm5.42 313 . 2  |-  ( (
ph  ->  ( ps  ->  ch ) )  <->  ( ph  ->  ( ps  ->  ( ph  /\  ch ) ) ) )
2 impexp 259 . 2  |-  ( ( ( ph  /\  ps )  ->  ( ph  /\  ch ) )  <->  ( ph  ->  ( ps  ->  ( ph  /\  ch ) ) ) )
31, 2bitr4i 185 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:  imdistand  436  pm5.3  459  rmoim  2814  ss2rab  3095  bezoutlembi  11087
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