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Theorem orri 367
Description: Infer implication from disjunction. (Contributed by NM, 11-Jun-1994.)
Hypothesis
Ref Expression
orri.1  |-  ( -. 
ph  ->  ps )
Assertion
Ref Expression
orri  |-  ( ph  \/  ps )

Proof of Theorem orri
StepHypRef Expression
1 orri.1 . 2  |-  ( -. 
ph  ->  ps )
2 df-or 361 . 2  |-  ( (
ph  \/  ps )  <->  ( -.  ph  ->  ps )
)
31, 2mpbir 202 1  |-  ( ph  \/  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 359
This theorem is referenced by:  orci  381  olci  382  pm2.25  395  exmid  406  pm2.13  409  pm3.12  488  pm5.11  856  pm5.12  857  pm5.14  858  pm5.15  861  pm5.55  869  pm5.54  872  rb-ax2  1528  rb-ax3  1529  rb-ax4  1530  exmo  2328  axi12  2417  axbnd  2418  abvor0  3647  ifeqor  3778  fvbr0  5754  letrii  9200
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 179  df-or 361
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