Theorem n0OLD 4349

Description: Obsolete version of n0 4346 as of 28-Jun-2024. (Contributed by NM, 29-Sep-2006.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
n0OLD	⊢ (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥 ∈ 𝐴)

Distinct variable group:   𝑥,𝐴

Proof of Theorem n0OLD

Step	Hyp	Ref	Expression
1		nfcv 2903	. 2 ⊢ Ⅎ𝑥𝐴
2	1	n0f 4342	1 ⊢ (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥 ∈ 𝐴)

Syntax hints:   ↔ wb 205  ∃wex 1781   ∈ wcel 2106   ≠ wne 2940  ∅c0 4322

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-11 2154  ax-12 2171  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-fal 1554  df-ex 1782  df-nf 1786  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-nfc 2885  df-ne 2941  df-dif 3951  df-nul 4323

This theorem is referenced by: (None)