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Theorem jaob 786
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 pm2.67-2 402 . . 3  |-  ( ( ( ph  \/  ch )  ->  ps )  -> 
( ph  ->  ps )
)
2 olc 384 . . . 4  |-  ( ch 
->  ( ph  \/  ch ) )
32imim1i 59 . . 3  |-  ( ( ( ph  \/  ch )  ->  ps )  -> 
( ch  ->  ps ) )
41, 3jca 532 . 2  |-  ( ( ( ph  \/  ch )  ->  ps )  -> 
( ( ph  ->  ps )  /\  ( ch 
->  ps ) ) )
5 pm3.44 511 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  ps ) )  ->  (
( ph  \/  ch )  ->  ps ) )
64, 5impbii 189 1  |-  ( ( ( ph  \/  ch )  ->  ps )  <->  ( ( ph  ->  ps )  /\  ( ch  ->  ps )
) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 186    \/ wo 368    /\ wa 369
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 187  df-or 370  df-an 371
This theorem is referenced by:  pm4.77  790  pm5.53  799  pm4.83  932  axio  2372  unss  3619  ralunb  3626  intun  4262  intpr  4263  relop  4976  sqrt2irr  14193  algcvgblem  14417  efgred  17092  caucfil  22016  plydivex  22987  2sqlem6  24027  arg-ax  30661  tendoeq2  33806  ifpidg  35595
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