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Theorem jaob 759
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 pm2.67-2 392 . . 3  |-  ( ( ( ph  \/  ch )  ->  ps )  -> 
( ph  ->  ps )
)
2 olc 374 . . . 4  |-  ( ch 
->  ( ph  \/  ch ) )
32imim1i 56 . . 3  |-  ( ( ( ph  \/  ch )  ->  ps )  -> 
( ch  ->  ps ) )
41, 3jca 519 . 2  |-  ( ( ( ph  \/  ch )  ->  ps )  -> 
( ( ph  ->  ps )  /\  ( ch 
->  ps ) ) )
5 pm3.44 498 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  ps ) )  ->  (
( ph  \/  ch )  ->  ps ) )
64, 5impbii 181 1  |-  ( ( ( ph  \/  ch )  ->  ps )  <->  ( ( ph  ->  ps )  /\  ( ch  ->  ps )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    \/ wo 358    /\ wa 359
This theorem is referenced by:  pm4.77  763  pm5.53  772  pm4.83  896  axio  2406  unss  3513  ralunb  3520  intun  4074  intpr  4075  relop  5014  sqr2irr  12836  algcvgblem  13056  efgred  15368  caucfil  19224  plydivex  20202  2sqlem6  21141  arg-ax  26114  tendoeq2  31410
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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