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Theorem jao 515
Description: Disjunction of antecedents. Compare Theorem *3.44 of [WhiteheadRussell] p. 113. (Contributed by NM, 5-Apr-1994.) (Proof shortened by Wolf Lammen, 4-Apr-2013.)
Assertion
Ref Expression
jao  |-  ( (
ph  ->  ps )  -> 
( ( ch  ->  ps )  ->  ( ( ph  \/  ch )  ->  ps ) ) )

Proof of Theorem jao
StepHypRef Expression
1 pm3.44 514 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  ps ) )  ->  (
( ph  \/  ch )  ->  ps ) )
21ex 436 1  |-  ( (
ph  ->  ps )  -> 
( ( ch  ->  ps )  ->  ( ( ph  \/  ch )  ->  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ wo 370
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:  3jao  1328  suctr  5505  en3lplem2  8117  indpi  9329  jaoded  36927  suctrALT2VD  37226  suctrALT2  37227  en3lplem2VD  37234  hbimpgVD  37295  ax6e2ndeqVD  37300  suctrALTcf  37313  suctrALTcfVD  37314  ax6e2ndeqALT  37322
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