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Theorem mt3 192
Description: A rule similar to modus tollens. Inference associated with con1i 144. (Contributed by NM, 18-May-1994.) (Proof shortened by Wolf Lammen, 11-Sep-2013.)
Hypotheses
Ref Expression
mt3.1 ¬ 𝜓
mt3.2 𝜑𝜓)
Assertion
Ref Expression
mt3 𝜑

Proof of Theorem mt3
StepHypRef Expression
1 mt3.1 . . 3 ¬ 𝜓
2 mt3.2 . . 3 𝜑𝜓)
31, 2mto 188 . 2 ¬ ¬ 𝜑
43notnotri 126 1 𝜑
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  7475  sinhalfpilem  24260  equidq  34528  etransc  40818
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