Theorem neq0OLD 4241

Description: Obsolete version of neq0 4238 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 2917	. 2 ⊢ Ⅎ𝑥𝐴
2	1	neq0f 4235	1 ⊢ (¬ 𝐴 = ∅ ↔ ∃𝑥 𝑥 ∈ 𝐴)

Syntax hints:  ¬ wn 3   ↔ wb 209   = wceq 1539  ∃wex 1782   ∈ wcel 2112  ∅c0 4221

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2114  ax-9 2122  ax-11 2159  ax-12 2176  ax-ext 2730

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 846  df-tru 1542  df-ex 1783  df-nf 1787  df-sb 2071  df-clab 2737  df-cleq 2751  df-clel 2831  df-nfc 2899  df-dif 3857  df-nul 4222

This theorem is referenced by: (None)