Theorem abfOLD

Description: Obsolete version of abf as of 28-Jun-2024. (Contributed by NM, 20-Jan-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	abfOLD.1	$$⊢\neg \phi$$
Assertion	abfOLD	$$⊢\left\{x|\phi \right\}=\varnothing$$

Proof

Step	Hyp	Ref	Expression
1		abfOLD.1	$$⊢\neg \phi$$
2		ab0	$$⊢\left\{x|\phi \right\}=\varnothing \leftrightarrow \forall x\neg \phi$$
3	2 1	mpgbir	$$⊢\left\{x|\phi \right\}=\varnothing$$