ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3jaoian Unicode version

Theorem 3jaoian 1266
Description: Disjunction of 3 antecedents (inference). (Contributed by NM, 14-Oct-2005.)
Hypotheses
Ref Expression
3jaoian.1  |-  ( (
ph  /\  ps )  ->  ch )
3jaoian.2  |-  ( ( th  /\  ps )  ->  ch )
3jaoian.3  |-  ( ( ta  /\  ps )  ->  ch )
Assertion
Ref Expression
3jaoian  |-  ( ( ( ph  \/  th  \/  ta )  /\  ps )  ->  ch )

Proof of Theorem 3jaoian
StepHypRef Expression
1 3jaoian.1 . . . 4  |-  ( (
ph  /\  ps )  ->  ch )
21ex 114 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 3jaoian.2 . . . 4  |-  ( ( th  /\  ps )  ->  ch )
43ex 114 . . 3  |-  ( th 
->  ( ps  ->  ch ) )
5 3jaoian.3 . . . 4  |-  ( ( ta  /\  ps )  ->  ch )
65ex 114 . . 3  |-  ( ta 
->  ( ps  ->  ch ) )
72, 4, 63jaoi 1264 . 2  |-  ( (
ph  \/  th  \/  ta )  ->  ( ps  ->  ch ) )
87imp 123 1  |-  ( ( ( ph  \/  th  \/  ta )  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    \/ w3o 944
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681
This theorem depends on definitions:  df-bi 116  df-3or 946  df-3an 947
This theorem is referenced by:  xrltnsym  9519  xrlttr  9521  xltnegi  9558  xaddcom  9584  xnegdi  9591  qbtwnxr  9975
  Copyright terms: Public domain W3C validator