Theorem eq0OLDOLD 4281

Description: Obsolete version of eq0 4277 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 2907	. 2 ⊢ Ⅎ𝑥𝐴
2	1	eq0f 4274	1 ⊢ (𝐴 = ∅ ↔ ∀𝑥 ¬ 𝑥 ∈ 𝐴)

Syntax hints:  ¬ wn 3   ↔ wb 205  ∀wal 1537   = wceq 1539   ∈ wcel 2106  ∅c0 4256

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-11 2154  ax-12 2171  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1542  df-fal 1552  df-ex 1783  df-nf 1787  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-nfc 2889  df-dif 3890  df-nul 4257

This theorem is referenced by: (None)