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Theorem ori 677
Description: Infer implication from disjunction. (Contributed by NM, 11-Jun-1994.) (Revised by Mario Carneiro, 31-Jan-2015.)
Hypothesis
Ref Expression
ori.1  |-  ( ph  \/  ps )
Assertion
Ref Expression
ori  |-  ( -. 
ph  ->  ps )

Proof of Theorem ori
StepHypRef Expression
1 ori.1 . 2  |-  ( ph  \/  ps )
2 pm2.53 676 . 2  |-  ( (
ph  \/  ps )  ->  ( -.  ph  ->  ps ) )
31, 2ax-mp 7 1  |-  ( -. 
ph  ->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 664
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 580  ax-io 665
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  3ori  1236  mtpor  1361  ax-12  1447  sbal1yz  1925  dvelimALT  1934  dvelimfv  1935
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