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Theorem 3jaoi 1303
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 1175 . 2  |-  ( (
ph  ->  ps )  /\  ( ch  ->  ps )  /\  ( th  ->  ps ) )
5 3jao 1301 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  ps )  /\  ( th 
->  ps ) )  -> 
( ( ph  \/  ch  \/  th )  ->  ps ) )
64, 5ax-mp 5 1  |-  ( (
ph  \/  ch  \/  th )  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ w3o 977    /\ w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709
This theorem depends on definitions:  df-bi 117  df-3or 979  df-3an 980
This theorem is referenced by:  3jaoian  1305  3ianorr  1309  acexmidlem1  5873  nndceq  6502  nndcel  6503  znegcl  9286  xrltnr  9781  nltpnft  9816  ngtmnft  9819  xrrebnd  9821  xnegcl  9834  xnegneg  9835  xltnegi  9837  xrpnfdc  9844  xrmnfdc  9845  xnegid  9861  xaddid1  9864  xposdif  9884  prm23lt5  12265  zabsle1  14439
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