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Theorem mt3 174
Description: A rule similar to modus tollens. (Contributed by NM, 18-May-1994.) (Proof shortened by Wolf Lammen, 11-Sep-2013.)
Hypotheses
Ref Expression
mt3.1  |-  -.  ps
mt3.2  |-  ( -. 
ph  ->  ps )
Assertion
Ref Expression
mt3  |-  ph

Proof of Theorem mt3
StepHypRef Expression
1 mt3.1 . . 3  |-  -.  ps
2 mt3.2 . . 3  |-  ( -. 
ph  ->  ps )
31, 2mto 170 . 2  |-  -.  -.  ph
43notnotri 109 1  |-  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  equidOLD  1690  spOLD  1765  spimehOLD  1841  cbv3hvOLD  1880  ax9OLD  2034  equidq  2254  sinhalfpilem  20376  wfrlem16  25555  cbv3hvNEW7  29508  ax9NEW7  29530
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
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