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Theorem mtand 640
Description: A modus tollens deduction. (Contributed by Jeff Hankins, 19-Aug-2009.)
Hypotheses
Ref Expression
mtand.1 (φ → ¬ χ)
mtand.2 ((φ ψ) → χ)
Assertion
Ref Expression
mtand (φ → ¬ ψ)

Proof of Theorem mtand
StepHypRef Expression
1 mtand.1 . 2 (φ → ¬ χ)
2 mtand.2 . . 3 ((φ ψ) → χ)
32ex 423 . 2 (φ → (ψχ))
41, 3mtod 168 1 (φ → ¬ ψ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
This theorem is referenced by:  tfinnn  4534  sfin111  4536  nchoicelem5  6293
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