Theorem eq0OLDOLD 4248

Description: Obsolete version of eq0 4244 as of 28-Jun-2024. (Contributed by NM, 29-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
eq0OLDOLD	⊢ (𝐴 = ∅ ↔ ∀𝑥 ¬ 𝑥 ∈ 𝐴)

Distinct variable group:   𝑥,𝐴

Proof of Theorem eq0OLDOLD

Step	Hyp	Ref	Expression
1		nfcv 2897	. 2 ⊢ Ⅎ𝑥𝐴
2	1	eq0f 4241	1 ⊢ (𝐴 = ∅ ↔ ∀𝑥 ¬ 𝑥 ∈ 𝐴)

Syntax hints:  ¬ wn 3   ↔ wb 209  ∀wal 1541   = wceq 1543   ∈ wcel 2112  ∅c0 4223

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2018  ax-8 2114  ax-9 2122  ax-11 2160  ax-12 2177  ax-ext 2708

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-tru 1546  df-fal 1556  df-ex 1788  df-nf 1792  df-sb 2073  df-clab 2715  df-cleq 2728  df-clel 2809  df-nfc 2879  df-dif 3856  df-nul 4224

This theorem is referenced by: (None)