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Theorem jaoian 782
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 434 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 jaoian.2 . . . 4  |-  ( ( th  /\  ps )  ->  ch )
43ex 434 . . 3  |-  ( th 
->  ( ps  ->  ch ) )
52, 4jaoi 379 . 2  |-  ( (
ph  \/  th )  ->  ( ps  ->  ch ) )
65imp 429 1  |-  ( ( ( ph  \/  th )  /\  ps )  ->  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ wo 368    /\ wa 369
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 185  df-or 370  df-an 371
This theorem is referenced by:  ccase  937  xaddnemnf  11319  xaddnepnf  11320  faclbnd  12187  faclbnd3  12189  faclbnd4lem1  12190  znf1o  18119  degltlem1  21686  ipasslem3  24412  xrge0iifhom  26535  fzsplit1nn0  29263
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