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	⊢ ¬ 𝜑
Assertion	bj-abf	⊢ { 𝑥 ∣ 𝜑 } = ∅

Proof

Step	Hyp	Ref	Expression
1		bj-abf.1	⊢ ¬ 𝜑
2		bj-ab0	⊢ ( ∀ 𝑥 ¬ 𝜑 → { 𝑥 ∣ 𝜑 } = ∅ )
3	2 1	mpg	⊢ { 𝑥 ∣ 𝜑 } = ∅