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Theorem mt3 183
Description: A rule similar to modus tollens. Inference associated with con1i 132. (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 179 . 2  |-  -.  -.  ph
43notnotri 117 1  |-  ph
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  wfrlem16  7059  sinhalfpilem  23283  equidq  32204  etransc  37715
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