Theorem bj-abf 36253

Description: Shorter proof of abf 4402 (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 36252	. 2 ⊢ (∀𝑥 ¬ 𝜑 → {𝑥 ∣ 𝜑} = ∅)
2		bj-abf.1	. 2 ⊢ ¬ 𝜑
3	1, 2	mpg 1798	1 ⊢ {𝑥 ∣ 𝜑} = ∅

Syntax hints:  ¬ wn 3   = wceq 1540  {cab 2708  ∅c0 4322

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-9 2115  ax-ext 2702

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1543  df-fal 1553  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723  df-dif 3951  df-nul 4323

This theorem is referenced by: (None)