MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  jaoian Unicode version

Theorem jaoian 759
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 423 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 jaoian.2 . . . 4  |-  ( ( th  /\  ps )  ->  ch )
43ex 423 . . 3  |-  ( th 
->  ( ps  ->  ch ) )
52, 4jaoi 368 . 2  |-  ( (
ph  \/  th )  ->  ( ps  ->  ch ) )
65imp 418 1  |-  ( ( ( ph  \/  th )  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 357    /\ wa 358
This theorem is referenced by:  ccase  912  xaddnemnf  10561  xaddnepnf  10562  faclbnd  11303  faclbnd3  11305  faclbnd4lem1  11306  znf1o  16505  degltlem1  19458  ipasslem3  21411  xrge0iifhom  23319  fzsplit1nn0  26833
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
  Copyright terms: Public domain W3C validator