Theorem bj-ntrufal 37050

Description: The negation of a theorem is equivalent to false. Shortens dfnul2 4297 (see bj-dfnul2 37051). (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 144	. 2 ⊢ ¬ ¬ 𝜑
3	2	bifal 1583	1 ⊢ (¬ 𝜑 ↔ ⊥)

Syntax hints:  ¬ wn 3   ↔ wb 209  ⊥wfal 1579

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  df-tru 1570  df-fal 1580

This theorem is referenced by:  bj-dfnul2  37051