Theorem bj-mt2bi 34435

Description: Version of mt2 203 where the major premise is a biconditional. Another proof is also possible via con2bii 361 and mpbi 233. The current mt2bi 367 should be relabeled, maybe to imfal. (Contributed by BJ, 5-Oct-2024.)

Hypotheses

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

Assertion

Ref	Expression
bj-mt2bi	⊢ ¬ 𝜓

Proof of Theorem bj-mt2bi

Step	Hyp	Ref	Expression
1		bj-mt2bi.min	. 2 ⊢ 𝜑
2		bj-mt2bi.maj	. . 3 ⊢ (𝜓 ↔ ¬ 𝜑)
3	2	biimpi 219	. 2 ⊢ (𝜓 → ¬ 𝜑)
4	1, 3	mt2 203	1 ⊢ ¬ 𝜓

Syntax hints:  ¬ wn 3   ↔ wb 209

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 210

This theorem is referenced by:  bj-fal  34437