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Theorem imdi 354
Description: Distributive law for implication. Compare Theorem *5.41 of [WhiteheadRussell] p. 125. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
imdi  |-  ( (
ph  ->  ( ps  ->  ch ) )  <->  ( ( ph  ->  ps )  -> 
( ph  ->  ch )
) )

Proof of Theorem imdi
StepHypRef Expression
1 ax-2 8 . 2  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( ph  ->  ps )  ->  ( ph  ->  ch ) ) )
2 pm2.86 96 . 2  |-  ( ( ( ph  ->  ps )  ->  ( ph  ->  ch ) )  ->  ( ph  ->  ( ps  ->  ch ) ) )
31, 2impbii 182 1  |-  ( (
ph  ->  ( ps  ->  ch ) )  <->  ( ( ph  ->  ps )  -> 
( ph  ->  ch )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178
This theorem is referenced by:  pm5.41  355  orimdi  823  bnj1174  28066
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
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