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Theorem neq0OLD 4308
Description: Obsolete version of neq0 4305 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 𝑥𝐴)
Distinct variable group:   𝑥,𝐴

Proof of Theorem neq0OLD
StepHypRef Expression
1 nfcv 2907 . 2 𝑥𝐴
21neq0f 4301 1 𝐴 = ∅ ↔ ∃𝑥 𝑥𝐴)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 205   = wceq 1541  wex 1781  wcel 2106  c0 4282
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 2707
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 2714  df-cleq 2728  df-clel 2814  df-nfc 2889  df-dif 3913  df-nul 4283
This theorem is referenced by: (None)
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