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Theorem mt2i 110
Description: Modus tollens inference. (Contributed by NM, 26-Mar-1995.) (Proof shortened by Wolf Lammen, 15-Sep-2012.)
Hypotheses
Ref Expression
mt2i.1  |-  ch
mt2i.2  |-  ( ph  ->  ( ps  ->  -.  ch ) )
Assertion
Ref Expression
mt2i  |-  ( ph  ->  -.  ps )

Proof of Theorem mt2i
StepHypRef Expression
1 mt2i.1 . . 3  |-  ch
21a1i 10 . 2  |-  ( ph  ->  ch )
3 mt2i.2 . 2  |-  ( ph  ->  ( ps  ->  -.  ch ) )
42, 3mt2d 109 1  |-  ( ph  ->  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  ssnlim  4690  elirrv  7327  konigthlem  8206  ipo0  27755  ifr0  27756  frgra2v  28423
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
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