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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  880  pm5.12  881  pm5.14  882  pm5.15  885  pm5.55  893  pm5.54  897  rb-ax2  1565  rb-ax3  1566  rb-ax4  1567  exmo  2297  axi12  2436  axbnd  2437  exmidne  2665  abvor0  3796  ifeqor  3976  fvbr0  5878  letrii  9698  numclwwlkdisj  24743
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