Theorem mt2i 645

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 9	. 2 ⊢ (𝜑 → 𝜒)
3		mt2i.2	. 2 ⊢ (𝜑 → (𝜓 → ¬ 𝜒))
4	2, 3	mt2d 626	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-in1 615  ax-in2 616

This theorem is referenced by:  0mnnnnn0  9298  climuni  11475  ennnfonelemk  12642