Theorem n0OLD 4280

Description: Obsolete version of n0 4277 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 2906	. 2 ⊢ Ⅎ𝑥𝐴
2	1	n0f 4273	1 ⊢ (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥 ∈ 𝐴)

Syntax hints:   ↔ wb 205  ∃wex 1783   ∈ wcel 2108   ≠ wne 2942  ∅c0 4253

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-11 2156  ax-12 2173  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1542  df-fal 1552  df-ex 1784  df-nf 1788  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-nfc 2888  df-ne 2943  df-dif 3886  df-nul 4254

This theorem is referenced by: (None)