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Theorem mt4i 131
Description: Modus tollens inference. (Contributed by Wolf Lammen, 12-May-2013.)
Hypotheses
Ref Expression
mt4i.1  |-  ch
mt4i.2  |-  ( ph  ->  ( -.  ps  ->  -. 
ch ) )
Assertion
Ref Expression
mt4i  |-  ( ph  ->  ps )

Proof of Theorem mt4i
StepHypRef Expression
1 mt4i.1 . . 3  |-  ch
21a1i 10 . 2  |-  ( ph  ->  ch )
3 mt4i.2 . 2  |-  ( ph  ->  ( -.  ps  ->  -. 
ch ) )
42, 3mt4d 130 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
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