Theorem abfOLD 4398

Description: Obsolete version of abf 4397 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 4369	. 2 ⊢ ({𝑥 ∣ 𝜑} = ∅ ↔ ∀𝑥 ¬ 𝜑)
2		abfOLD.1	. 2 ⊢ ¬ 𝜑
3	1, 2	mpgbir 1793	1 ⊢ {𝑥 ∣ 𝜑} = ∅

Syntax hints:  ¬ wn 3   = wceq 1533  {cab 2703  ∅c0 4317

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-ext 2697

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2704  df-cleq 2718  df-dif 3946  df-nul 4318

This theorem is referenced by: (None)