Theorem neq0OLD 4287

Description: Obsolete version of neq0 4284 as of 28-Jun-2024. (Contributed by NM, 21-Jun-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
neq0OLD	⊢ (¬ 𝐴 = ∅ ↔ ∃𝑥 𝑥 ∈ 𝐴)

Distinct variable group:   𝑥,𝐴

Proof of Theorem neq0OLD

Step	Hyp	Ref	Expression
1		nfcv 2908	. 2 ⊢ Ⅎ𝑥𝐴
2	1	neq0f 4280	1 ⊢ (¬ 𝐴 = ∅ ↔ ∃𝑥 𝑥 ∈ 𝐴)

Syntax hints:  ¬ wn 3   ↔ wb 205   = wceq 1541  ∃wex 1785   ∈ wcel 2109  ∅c0 4261

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1801  ax-4 1815  ax-5 1916  ax-6 1974  ax-7 2014  ax-8 2111  ax-9 2119  ax-11 2157  ax-12 2174  ax-ext 2710

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1544  df-fal 1554  df-ex 1786  df-nf 1790  df-sb 2071  df-clab 2717  df-cleq 2731  df-clel 2817  df-nfc 2890  df-dif 3894  df-nul 4262

This theorem is referenced by: (None)