Theorem bj-ntrufal 37219

Description: The negation of a theorem is equivalent to false. Shortens dfnul2 4289 (see bj-dfnul2 37220). (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 1586	1 ⊢ (¬ 𝜑 ↔ ⊥)

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 209  ⊥wfal 1582

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-tru 1573  df-fal 1583

This theorem is used by:  bj-dfnul2  37220