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Theorem imorri 701
Description: Infer implication from disjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Revised by Mario Carneiro, 31-Jan-2015.)
Hypothesis
Ref Expression
imorri.1  |-  ( -. 
ph  \/  ps )
Assertion
Ref Expression
imorri  |-  ( ph  ->  ps )

Proof of Theorem imorri
StepHypRef Expression
1 imorri.1 . 2  |-  ( -. 
ph  \/  ps )
2 pm2.21 580 . . 3  |-  ( -. 
ph  ->  ( ph  ->  ps ) )
3 ax-1 5 . . 3  |-  ( ps 
->  ( ph  ->  ps ) )
42, 3jaoi 669 . 2  |-  ( ( -.  ph  \/  ps )  ->  ( ph  ->  ps ) )
51, 4ax-mp 7 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 662
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 578  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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