Theorem mt3i

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

	Ref	Expression
Hypotheses	mt3i.1	⊢ ¬ 𝜒
	mt3i.2	⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜒 ) )
Assertion	mt3i	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		mt3i.1	⊢ ¬ 𝜒
2		mt3i.2	⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜒 ) )
3	1	a1i	⊢ ( 𝜑 → ¬ 𝜒 )
4	3 2	mt3d	⊢ ( 𝜑 → 𝜓 )