Theorem mt2i

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

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

Proof

Step	Hyp	Ref	Expression
1		mt2i.1	⊢ 𝜒
2		mt2i.2	⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜒 ) )
3	1	a1i	⊢ ( 𝜑 → 𝜒 )
4	3 2	mt2d	⊢ ( 𝜑 → ¬ 𝜓 )