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Theorem 3jaoi 1209
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 1093 . 2  |-  ( (
ph  ->  ps )  /\  ( ch  ->  ps )  /\  ( th  ->  ps ) )
5 3jao 1207 . 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 895    /\ w3a 896
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:  3jaoian  1211  3ianorr  1215  sspsstrir  3074  acexmidlem1  5536  nndceq  6108  nndcel  6109  znegcl  8333  xrltnr  8802  nltpnft  8831  ngtmnft  8832  xrrebnd  8833  xnegcl  8846  xnegneg  8847  xltnegi  8849
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