Theorem abfOLD 4334

Description: Obsolete version of abf 4333 as of 28-Jun-2024. (Contributed by NM, 20-Jan-2012.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
abfOLD.1	⊢ ¬ 𝜑

Assertion

Ref	Expression
abfOLD	⊢ {𝑥 ∣ 𝜑} = ∅

Proof of Theorem abfOLD

Step	Hyp	Ref	Expression
1		ab0 4305	. 2 ⊢ ({𝑥 ∣ 𝜑} = ∅ ↔ ∀𝑥 ¬ 𝜑)
2		abfOLD.1	. 2 ⊢ ¬ 𝜑
3	1, 2	mpgbir 1803	1 ⊢ {𝑥 ∣ 𝜑} = ∅

Syntax hints:  ¬ wn 3   = wceq 1539  {cab 2715  ∅c0 4253

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-9 2118  ax-10 2139  ax-11 2156  ax-12 2173  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1542  df-fal 1552  df-ex 1784  df-nf 1788  df-sb 2069  df-clab 2716  df-cleq 2730  df-dif 3886  df-nul 4254

This theorem is referenced by: (None)