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Theorem mt4 129
Description: The rule of modus tollens. (Contributed by Wolf Lammen, 12-May-2013.)
Hypotheses
Ref Expression
mt4.1  |-  ph
mt4.2  |-  ( -. 
ps  ->  -.  ph )
Assertion
Ref Expression
mt4  |-  ps

Proof of Theorem mt4
StepHypRef Expression
1 mt4.1 . 2  |-  ph
2 mt4.2 . . 3  |-  ( -. 
ps  ->  -.  ph )
32con4i 122 . 2  |-  ( ph  ->  ps )
41, 3ax-mp 8 1  |-  ps
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  infeq5i  7337  chirredi  22974
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
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