Theorem mtbird

Description: A deduction from a biconditional, similar to modus tollens. (Contributed by NM, 10-May-1994)

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

Proof

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