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Theorem jao 500
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 pm3.44 499 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  ps ) )  ->  (
( ph  \/  ch )  ->  ps ) )
21ex 425 1  |-  ( (
ph  ->  ps )  -> 
( ( ch  ->  ps )  ->  ( ( ph  \/  ch )  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    \/ wo 359
This theorem is referenced by:  3jao  1248  suctr  4474  en3lplem2  7412  indpi  8526  jaoded  27603  suctrALT2VD  27880  suctrALT2  27881  en3lplem2VD  27888  hbimpgVD  27948  a9e2ndeqVD  27953  suctrALTcf  27966  suctrALTcfVD  27967  suctrALT4  27972  a9e2ndeqALT  27976
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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