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Theorem jaoian 785
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 432 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 jaoian.2 . . . 4  |-  ( ( th  /\  ps )  ->  ch )
43ex 432 . . 3  |-  ( th 
->  ( ps  ->  ch ) )
52, 4jaoi 377 . 2  |-  ( (
ph  \/  th )  ->  ( ps  ->  ch ) )
65imp 427 1  |-  ( ( ( ph  \/  th )  /\  ps )  ->  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ wo 366    /\ wa 367
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 368  df-an 369
This theorem is referenced by:  ccase  947  tpres  6104  xaddnemnf  11486  xaddnepnf  11487  faclbnd  12412  faclbnd3  12414  faclbnd4lem1  12415  znf1o  18888  degltlem1  22764  ipasslem3  26162  padct  27992  fz1nntr  28055  xrge0iifhom  28372  fzsplit1nn0  35048
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