Theorem abfOLD 4337

Description: Obsolete version of abf 4336 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 4308	. 2 ⊢ ({𝑥 ∣ 𝜑} = ∅ ↔ ∀𝑥 ¬ 𝜑)
2		abfOLD.1	. 2 ⊢ ¬ 𝜑
3	1, 2	mpgbir 1802	1 ⊢ {𝑥 ∣ 𝜑} = ∅

Syntax hints:  ¬ wn 3   = wceq 1539  {cab 2715  ∅c0 4256

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1542  df-fal 1552  df-ex 1783  df-nf 1787  df-sb 2068  df-clab 2716  df-cleq 2730  df-dif 3890  df-nul 4257

This theorem is referenced by: (None)