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Theorem ori 712
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 pm2.53 711 . 2  |-  ( (
ph  \/  ps )  ->  ( -.  ph  ->  ps ) )
31, 2ax-mp 5 1  |-  ( -. 
ph  ->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 697
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 604  ax-io 698
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  3ori  1278  mtpor  1403  ax-12  1489  sbal1yz  1976  dvelimALT  1985  dvelimfv  1986
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