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Theorem mtord 641
Description: A modus tollens deduction involving disjunction. (Contributed by Jeff Hankins, 15-Jul-2009.)
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.2 . 2  |-  ( ph  ->  -.  th )
2 mtord.1 . . 3  |-  ( ph  ->  -.  ch )
3 mtord.3 . . . 4  |-  ( ph  ->  ( ps  ->  ( ch  \/  th ) ) )
4 df-or 359 . . . 4  |-  ( ( ch  \/  th )  <->  ( -.  ch  ->  th )
)
53, 4syl6ib 217 . . 3  |-  ( ph  ->  ( ps  ->  ( -.  ch  ->  th )
) )
62, 5mpid 37 . 2  |-  ( ph  ->  ( ps  ->  th )
)
71, 6mtod 168 1  |-  ( ph  ->  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 357
This theorem is referenced by:  swoer  6688  inar1  8397  mtordOLD  26218
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359
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