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

Theorem 3jaoi 1239
Description: Disjunction of 3 antecedents (inference). (Contributed by NM, 12-Sep-1995.)
Hypotheses
Ref Expression
3jaoi.1  |-  ( ph  ->  ps )
3jaoi.2  |-  ( ch 
->  ps )
3jaoi.3  |-  ( th 
->  ps )
Assertion
Ref Expression
3jaoi  |-  ( (
ph  \/  ch  \/  th )  ->  ps )

Proof of Theorem 3jaoi
StepHypRef Expression
1 3jaoi.1 . . 3  |-  ( ph  ->  ps )
2 3jaoi.2 . . 3  |-  ( ch 
->  ps )
3 3jaoi.3 . . 3  |-  ( th 
->  ps )
41, 2, 33pm3.2i 1121 . 2  |-  ( (
ph  ->  ps )  /\  ( ch  ->  ps )  /\  ( th  ->  ps ) )
5 3jao 1237 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  ps )  /\  ( th 
->  ps ) )  -> 
( ( ph  \/  ch  \/  th )  ->  ps ) )
64, 5ax-mp 7 1  |-  ( (
ph  \/  ch  \/  th )  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ w3o 923    /\ w3a 924
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665
This theorem depends on definitions:  df-bi 115  df-3or 925  df-3an 926
This theorem is referenced by:  3jaoian  1241  3ianorr  1245  acexmidlem1  5648  nndceq  6260  nndcel  6261  znegcl  8779  xrltnr  9248  nltpnft  9277  ngtmnft  9278  xrrebnd  9279  xnegcl  9292  xnegneg  9293  xltnegi  9295
  Copyright terms: Public domain W3C validator