Theorem mtbi

Description: An inference from a biconditional, related to modus tollens. (Contributed by NM, 15-Nov-1994) (Proof shortened by Wolf Lammen, 25-Oct-2012)

	Ref	Expression
Hypotheses	mtbi.1	⊢ ¬ 𝜑
	mtbi.2	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	mtbi	⊢ ¬ 𝜓

Proof

Step	Hyp	Ref	Expression
1		mtbi.1	⊢ ¬ 𝜑
2		mtbi.2	⊢ ( 𝜑 ↔ 𝜓 )
3	2	biimpri	⊢ ( 𝜓 → 𝜑 )
4	1 3	mto	⊢ ¬ 𝜓