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Theorem jaob 791
Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. (Contributed by NM, 30-May-1994.) (Proof shortened by Wolf Lammen, 9-Dec-2012.)
Assertion
Ref Expression
jaob  |-  ( ( ( ph  \/  ch )  ->  ps )  <->  ( ( ph  ->  ps )  /\  ( ch  ->  ps )
) )

Proof of Theorem jaob
StepHypRef Expression
1 pm2.67-2 404 . . 3  |-  ( ( ( ph  \/  ch )  ->  ps )  -> 
( ph  ->  ps )
)
2 olc 386 . . . 4  |-  ( ch 
->  ( ph  \/  ch ) )
32imim1i 61 . . 3  |-  ( ( ( ph  \/  ch )  ->  ps )  -> 
( ch  ->  ps ) )
41, 3jca 535 . 2  |-  ( ( ( ph  \/  ch )  ->  ps )  -> 
( ( ph  ->  ps )  /\  ( ch 
->  ps ) ) )
5 pm3.44 514 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  ps ) )  ->  (
( ph  \/  ch )  ->  ps ) )
64, 5impbii 191 1  |-  ( ( ( ph  \/  ch )  ->  ps )  <->  ( ( ph  ->  ps )  /\  ( ch  ->  ps )
) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 188    \/ wo 370    /\ wa 371
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 189  df-or 372  df-an 373
This theorem is referenced by:  pm4.77  795  pm5.53  804  pm4.83  938  axio  2391  unss  3641  ralunb  3648  intun  4286  intpr  4287  relop  5002  sqrt2irr  14294  algcvgblem  14529  efgred  17391  caucfil  22245  plydivex  23242  2sqlem6  24289  arg-ax  31075  tendoeq2  34266  ifpidg  36061
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