Theorem eq0OLDOLD 4343

Description: Obsolete version of eq0 4339 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 2892	. 2 ⊢ Ⅎ𝑥𝐴
2	1	eq0f 4336	1 ⊢ (𝐴 = ∅ ↔ ∀𝑥 ¬ 𝑥 ∈ 𝐴)

Syntax hints:  ¬ wn 3   ↔ wb 205  ∀wal 1531   = wceq 1533   ∈ wcel 2098  ∅c0 4318

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-8 2100  ax-9 2108  ax-11 2146  ax-12 2166  ax-ext 2696

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-nfc 2877  df-dif 3942  df-nul 4319

This theorem is referenced by: (None)