Theorem bj-abf

Description: Shorter proof of abf (which should be kept as abfALT). (Contributed by BJ, 24-Jul-2019) (Proof modification is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		bj-abf.1	$$⊢\neg \phi$$
2		bj-ab0	$$⊢\forall x\neg \phi \to \left\{x|\phi \right\}=\varnothing$$
3	2 1	mpg	$$⊢\left\{x|\phi \right\}=\varnothing$$