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Theorem n0OLD 4345
Description: Obsolete version of n0 4342 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 𝑥𝐴)
Distinct variable group:   𝑥,𝐴

Proof of Theorem n0OLD
StepHypRef Expression
1 nfcv 2899 . 2 𝑥𝐴
21n0f 4338 1 (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥𝐴)
Colors of variables: wff setvar class
Syntax hints:  wb 205  wex 1774  wcel 2099  wne 2936  c0 4318
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-11 2147  ax-12 2167  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-tru 1537  df-fal 1547  df-ex 1775  df-nf 1779  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-nfc 2881  df-ne 2937  df-dif 3948  df-nul 4319
This theorem is referenced by: (None)
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