Theorem mtoi

Description: Modus tollens inference. (Contributed by NM, 5-Jul-1994) (Proof shortened by Wolf Lammen, 15-Sep-2012)

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

Proof

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