Theorem mt4i 118

Description: Modus tollens inference. (Contributed by Wolf Lammen, 12-May-2013.)

Hypotheses

Ref	Expression
mt4i.1	⊢ 𝜒
mt4i.2	⊢ (𝜑 → (¬ 𝜓 → ¬ 𝜒))

Assertion

Ref	Expression
mt4i	⊢ (𝜑 → 𝜓)

Proof of Theorem mt4i

Step	Hyp	Ref	Expression
1		mt4i.1	. . 3 ⊢ 𝜒
2	1	a1i 11	. 2 ⊢ (𝜑 → 𝜒)
3		mt4i.2	. 2 ⊢ (𝜑 → (¬ 𝜓 → ¬ 𝜒))
4	2, 3	mt4d 117	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:  0mnnnnn0  12265