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Theorem jaoian 760
Description: Inference disjoining the antecedents of two implications. (Contributed by NM, 23-Oct-2005.)
Hypotheses
Ref Expression
jaoian.1  |-  ( (
ph  /\  ps )  ->  ch )
jaoian.2  |-  ( ( th  /\  ps )  ->  ch )
Assertion
Ref Expression
jaoian  |-  ( ( ( ph  \/  th )  /\  ps )  ->  ch )

Proof of Theorem jaoian
StepHypRef Expression
1 jaoian.1 . . . 4  |-  ( (
ph  /\  ps )  ->  ch )
21ex 424 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 jaoian.2 . . . 4  |-  ( ( th  /\  ps )  ->  ch )
43ex 424 . . 3  |-  ( th 
->  ( ps  ->  ch ) )
52, 4jaoi 369 . 2  |-  ( (
ph  \/  th )  ->  ( ps  ->  ch ) )
65imp 419 1  |-  ( ( ( ph  \/  th )  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 358    /\ wa 359
This theorem is referenced by:  ccase  913  xaddnemnf  10820  xaddnepnf  10821  faclbnd  11581  faclbnd3  11583  faclbnd4lem1  11584  znf1o  16832  degltlem1  19995  ipasslem3  22334  xrge0iifhom  24323  fzsplit1nn0  26812
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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