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Theorem jaob 761
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 pm2.67-2 393 . . 3  |-  ( ( ( ph  \/  ch )  ->  ps )  -> 
( ph  ->  ps )
)
2 olc 375 . . . 4  |-  ( ch 
->  ( ph  \/  ch ) )
32imim1i 56 . . 3  |-  ( ( ( ph  \/  ch )  ->  ps )  -> 
( ch  ->  ps ) )
41, 3jca 520 . 2  |-  ( ( ( ph  \/  ch )  ->  ps )  -> 
( ( ph  ->  ps )  /\  ( ch 
->  ps ) ) )
5 pm3.44 499 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  ps ) )  ->  (
( ph  \/  ch )  ->  ps ) )
64, 5impbii 182 1  |-  ( ( ( ph  \/  ch )  ->  ps )  <->  ( ( ph  ->  ps )  /\  ( ch  ->  ps )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178    \/ wo 359    /\ wa 360
This theorem is referenced by:  pm4.77  765  pm5.53  774  pm4.83  900  unss  3310  ralunb  3317  intun  3854  intpr  3855  relop  4808  sqr2irr  12475  algcvgblem  12695  efgred  15005  caucfil  18657  plydivex  19625  2sqlem6  20556  arg-ax  24216  domrngref  24412  a12study4  28268  tendoeq2  30114
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362
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