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

Step	Hyp	Ref	Expression
1		mtand.1	. 2 ⊢ (φ → ¬ χ)
2		mtand.2	. . 3 ⊢ ((φ ∧ ψ) → χ)
3	2	ex 423	. 2 ⊢ (φ → (ψ → χ))
4	1, 3	mtod 168	1 ⊢ (φ → ¬ ψ)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  tfinnn  4534  sfin111  4536  nchoicelem5  6293