Theorem mt2i 110

Description: Modus tollens inference. (Contributed by NM, 26-Mar-1995.) (Proof shortened by Wolf Lammen, 15-Sep-2012.)

Hypotheses

Ref	Expression
mt2i.1	⊢ χ
mt2i.2	⊢ (φ → (ψ → ¬ χ))

Assertion

Ref	Expression
mt2i	⊢ (φ → ¬ ψ)

Proof of Theorem mt2i

Step	Hyp	Ref	Expression
1		mt2i.1	. . 3 ⊢ χ
2	1	a1i 10	. 2 ⊢ (φ → χ)
3		mt2i.2	. 2 ⊢ (φ → (ψ → ¬ χ))
4	2, 3	mt2d 109	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: (None)