Theorem bj-ntrufal 34729

Description: The negation of a theorem is equivalent to false. This can shorten dfnul2 4264. (Contributed by BJ, 5-Oct-2024.)

Hypothesis

Ref	Expression
bj-ntrufal.1	⊢ 𝜑

Assertion

Ref	Expression
bj-ntrufal	⊢ (¬ 𝜑 ↔ ⊥)

Proof of Theorem bj-ntrufal

Step	Hyp	Ref	Expression
1		bj-ntrufal.1	. . 3 ⊢ 𝜑
2	1	notnoti 143	. 2 ⊢ ¬ ¬ 𝜑
3	2	bifal 1557	1 ⊢ (¬ 𝜑 ↔ ⊥)

Syntax hints:  ¬ wn 3   ↔ wb 205  ⊥wfal 1553

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 206  df-tru 1544  df-fal 1554

This theorem is referenced by: (None)