Theorem bj-ntrufal

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

	Ref	Expression
Hypothesis	bj-ntrufal.1	⊢ 𝜑
Assertion	bj-ntrufal	⊢ ( ¬ 𝜑 ↔ ⊥ )

Proof

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