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

Theorem 3jaoian 1211
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 112 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 3jaoian.2 . . . 4  |-  ( ( th  /\  ps )  ->  ch )
43ex 112 . . 3  |-  ( th 
->  ( ps  ->  ch ) )
5 3jaoian.3 . . . 4  |-  ( ( ta  /\  ps )  ->  ch )
65ex 112 . . 3  |-  ( ta 
->  ( ps  ->  ch ) )
72, 4, 63jaoi 1209 . 2  |-  ( (
ph  \/  th  \/  ta )  ->  ( ps  ->  ch ) )
87imp 119 1  |-  ( ( ( ph  \/  th  \/  ta )  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101    \/ w3o 895
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640
This theorem depends on definitions:  df-bi 114  df-3or 897  df-3an 898
This theorem is referenced by:  xrltnsym  8815  xrlttr  8817  xltnegi  8849  qbtwnxr  9214
  Copyright terms: Public domain W3C validator