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Theorem mtord 730
Description: A modus tollens deduction involving disjunction. (Contributed by Jeff Hankins, 15-Jul-2009.) (Revised by Mario Carneiro, 31-Jan-2015.)
Hypotheses
Ref Expression
mtord.1  |-  ( ph  ->  -.  ch )
mtord.2  |-  ( ph  ->  -.  th )
mtord.3  |-  ( ph  ->  ( ps  ->  ( ch  \/  th ) ) )
Assertion
Ref Expression
mtord  |-  ( ph  ->  -.  ps )

Proof of Theorem mtord
StepHypRef Expression
1 mtord.3 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  \/  th ) ) )
2 mtord.1 . . . . 5  |-  ( ph  ->  -.  ch )
32pm2.21d 582 . . . 4  |-  ( ph  ->  ( ch  ->  -.  ps ) )
4 mtord.2 . . . . 5  |-  ( ph  ->  -.  th )
54pm2.21d 582 . . . 4  |-  ( ph  ->  ( th  ->  -.  ps ) )
63, 5jaod 670 . . 3  |-  ( ph  ->  ( ( ch  \/  th )  ->  -.  ps )
)
71, 6syld 44 . 2  |-  ( ph  ->  ( ps  ->  -.  ps ) )
87pm2.01d 581 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-in1 577  ax-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  swoer  6193
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