Theorem bj-abf 36387

Description: Shorter proof of abf 4403 (which should be kept as abfALT). (Contributed by BJ, 24-Jul-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-abf.1	⊢ ¬ 𝜑

Assertion

Ref	Expression
bj-abf	⊢ {𝑥 ∣ 𝜑} = ∅

Proof of Theorem bj-abf

Step	Hyp	Ref	Expression
1		bj-ab0 36386	. 2 ⊢ (∀𝑥 ¬ 𝜑 → {𝑥 ∣ 𝜑} = ∅)
2		bj-abf.1	. 2 ⊢ ¬ 𝜑
3	1, 2	mpg 1792	1 ⊢ {𝑥 ∣ 𝜑} = ∅

Syntax hints:  ¬ wn 3   = wceq 1534  {cab 2705  ∅c0 4323

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-9 2109  ax-ext 2699

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-dif 3950  df-nul 4324

This theorem is referenced by: (None)