Theorem mtbii

Description: An inference from a biconditional, similar to modus tollens. (Contributed by NM, 27-Nov-1995)

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

Proof

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