Theorem bj-mt2bi

Description: Version of mt2 where the major premise is a biconditional. Shortens fal (see bj-fal ) . Another proof is also possible via con2bii and mpbi . The current mt2bi should be relabeled, maybe to imfal. (Contributed by BJ, 5-Oct-2024)

	Ref	Expression
Hypotheses	bj-mt2bi.maj	⊢ ( 𝜓 ↔ ¬ 𝜑 )
	bj-mt2bi.min	⊢ 𝜑
Assertion	bj-mt2bi	⊢ ¬ 𝜓

Proof

Step	Hyp	Ref	Expression
1		bj-mt2bi.maj	⊢ ( 𝜓 ↔ ¬ 𝜑 )
2		bj-mt2bi.min	⊢ 𝜑
3	1	biimpi	⊢ ( 𝜓 → ¬ 𝜑 )
4	2 3	mt2	⊢ ¬ 𝜓