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	$$⊢\phi$$
Assertion	bj-ntrufal	$$⊢\neg \phi \leftrightarrow \perp$$

Proof

Step	Hyp	Ref	Expression
1		bj-ntrufal.1	$$⊢\phi$$
2	1	notnoti	$$⊢\neg \neg \phi$$
3	2	bifal	$$⊢\neg \phi \leftrightarrow \perp$$