Theorem mtbiri

Description: An inference from a biconditional, similar to modus tollens. (Contributed by NM, 24-Aug-1995)

	Ref	Expression
Hypotheses	mtbiri.min	⊢ ¬ 𝜒
	mtbiri.maj	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
Assertion	mtbiri	⊢ ( 𝜑 → ¬ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		mtbiri.min	⊢ ¬ 𝜒
2		mtbiri.maj	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
3	2	biimpd	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4	1 3	mtoi	⊢ ( 𝜑 → ¬ 𝜓 )