Theorem mt3d 117

Description: Modus tollens deduction. (Contributed by NM, 26-Mar-1995.)

Hypotheses

Ref	Expression
mt3d.1	⊢ (φ → ¬ χ)
mt3d.2	⊢ (φ → (¬ ψ → χ))

Assertion

Ref	Expression
mt3d	⊢ (φ → ψ)

Proof of Theorem mt3d

Step	Hyp	Ref	Expression
1		mt3d.1	. 2 ⊢ (φ → ¬ χ)
2		mt3d.2	. . 3 ⊢ (φ → (¬ ψ → χ))
3	2	con1d 116	. 2 ⊢ (φ → (¬ χ → ψ))
4	1, 3	mpd 14	1 ⊢ (φ → ψ)

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:  mt3i  118  nsyl2  119  ecase23d  1285  nnsucelr  4429  enprmaplem5  6081