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Theorem mt3i 151
Description: Modus tollens inference. (Contributed by NM, 26-Mar-1995.) (Proof shortened by Wolf Lammen, 15-Sep-2012.)
Hypotheses
Ref Expression
mt3i.1 ¬ 𝜒
mt3i.2 (𝜑 → (¬ 𝜓𝜒))
Assertion
Ref Expression
mt3i (𝜑𝜓)

Proof of Theorem mt3i
StepHypRef Expression
1 mt3i.1 . . 3 ¬ 𝜒
21a1i 11 . 2 (𝜑 → ¬ 𝜒)
3 mt3i.2 . 2 (𝜑 → (¬ 𝜓𝜒))
42, 3mt3d 150 1 (𝜑𝜓)
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:  biorfi  938  ordeleqon  7535  wofib  9095  harcard  9493  infpssALT  9826  zorn2lem4  10012  lt6abl  19147  gzrngunitlem  20295  bwth  22174  i1f0rn  24447  dfon2lem3  33348  slerec  33669  poimirlem30  35463
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