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Theorem jao 498
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 pm3.44 497 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  ps ) )  ->  (
( ph  \/  ch )  ->  ps ) )
21ex 423 1  |-  ( (
ph  ->  ps )  -> 
( ( ch  ->  ps )  ->  ( ( ph  \/  ch )  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 357
This theorem is referenced by:  3jao  1243  suctr  4491  en3lplem2  7433  indpi  8547  jaoded  28631  suctrALT2VD  28928  suctrALT2  28929  en3lplem2VD  28936  hbimpgVD  28996  a9e2ndeqVD  29001  suctrALTcf  29014  suctrALTcfVD  29015  suctrALT4  29020  a9e2ndeqALT  29024
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 177  df-or 359  df-an 360
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