Theorem mt2d 109

Description: Modus tollens deduction. (Contributed by NM, 4-Jul-1994.)

Hypotheses

Ref	Expression
mt2d.1	⊢ (φ → χ)
mt2d.2	⊢ (φ → (ψ → ¬ χ))

Assertion

Ref	Expression
mt2d	⊢ (φ → ¬ ψ)

Proof of Theorem mt2d

Step	Hyp	Ref	Expression
1		mt2d.1	. 2 ⊢ (φ → χ)
2		mt2d.2	. . 3 ⊢ (φ → (ψ → ¬ χ))
3	2	con2d 107	. 2 ⊢ (φ → (χ → ¬ ψ))
4	1, 3	mpd 14	1 ⊢ (φ → ¬ ψ)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is used by:  mt2i  110  nsyl3  111