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Theorem pm5.6 879
Description: Conjunction in antecedent versus disjunction in consequent. Theorem *5.6 of [WhiteheadRussell] p. 125. (Contributed by NM, 8-Jun-1994.)
Assertion
Ref Expression
pm5.6  |-  ( ( ( ph  /\  -.  ps )  ->  ch )  <->  (
ph  ->  ( ps  \/  ch ) ) )

Proof of Theorem pm5.6
StepHypRef Expression
1 impexp 434 . 2  |-  ( ( ( ph  /\  -.  ps )  ->  ch )  <->  (
ph  ->  ( -.  ps  ->  ch ) ) )
2 df-or 360 . . 3  |-  ( ( ps  \/  ch )  <->  ( -.  ps  ->  ch ) )
32imbi2i 304 . 2  |-  ( (
ph  ->  ( ps  \/  ch ) )  <->  ( ph  ->  ( -.  ps  ->  ch ) ) )
41, 3bitr4i 244 1  |-  ( ( ( ph  /\  -.  ps )  ->  ch )  <->  (
ph  ->  ( ps  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 177    \/ wo 358    /\ wa 359
This theorem is referenced by:  ssundif  3654  brdom3  8339  grothprim  8642  eliccelico  23976  elicoelioo  23977  ballotlemfc0  24529  ballotlemfcc  24530  elicc3  26011
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361
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