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Theorem pm5.6 913
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 444 . 2  |-  ( ( ( ph  /\  -.  ps )  ->  ch )  <->  (
ph  ->  ( -.  ps  ->  ch ) ) )
2 df-or 368 . . 3  |-  ( ( ps  \/  ch )  <->  ( -.  ps  ->  ch ) )
32imbi2i 310 . 2  |-  ( (
ph  ->  ( ps  \/  ch ) )  <->  ( ph  ->  ( -.  ps  ->  ch ) ) )
41, 3bitr4i 252 1  |-  ( ( ( ph  /\  -.  ps )  ->  ch )  <->  (
ph  ->  ( ps  \/  ch ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 184    \/ wo 366    /\ wa 367
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369
This theorem is referenced by:  ssundif  3855  brdom3  8938  grothprim  9242  eliccelico  28036  elicoelioo  28037  ballotlemfc0  28937  ballotlemfcc  28938  elicc3  30545  ifpidg  35582  icccncfext  37058
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