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Theorem mt3i 118
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 10 . 2 (φ → ¬ χ)
3 mt3i.2 . 2 (φ → (¬ ψχ))
42, 3mt3d 117 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: (None)
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