Theorem mtbid

Description: A deduction from a biconditional, similar to modus tollens. (Contributed by NM, 26-Nov-1995)

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

Proof

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