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Theorem orri 376
Description: Infer disjunction from implication. (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 370 . 2  |-  ( (
ph  \/  ps )  <->  ( -.  ph  ->  ps )
)
31, 2mpbir 209 1  |-  ( ph  \/  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 368
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-or 370
This theorem is referenced by:  orci  390  olci  391  pm2.25  404  exmid  415  pm2.13  418  pm3.12  500  pm5.11  879  pm5.12  880  pm5.14  881  pm5.15  884  pm5.55  892  pm5.54  895  rb-ax2  1561  rb-ax3  1562  rb-ax4  1563  exmo  2291  axi12  2430  axbnd  2431  exmidne  2658  abvor0  3764  ifeqor  3942  fvbr0  5821  letrii  9611  numclwwlkdisj  30822
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