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Theorem n0r 3340
 Description: An inhabited class is nonempty. See n0rf 3339 for more discussion. (Contributed by Jim Kingdon, 31-Jul-2018.)
Assertion
Ref Expression
n0r (∃𝑥 𝑥𝐴𝐴 ≠ ∅)
Distinct variable group:   𝑥,𝐴

Proof of Theorem n0r
StepHypRef Expression
1 nfcv 2253 . 2 𝑥𝐴
21n0rf 3339 1 (∃𝑥 𝑥𝐴𝐴 ≠ ∅)
 Colors of variables: wff set class Syntax hints:   → wi 4  ∃wex 1449   ∈ wcel 1461   ≠ wne 2280  ∅c0 3327 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681  ax-5 1404  ax-7 1405  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-10 1464  ax-11 1465  ax-i12 1466  ax-bndl 1467  ax-4 1468  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-i5r 1496  ax-ext 2095 This theorem depends on definitions:  df-bi 116  df-tru 1315  df-fal 1318  df-nf 1418  df-sb 1717  df-clab 2100  df-cleq 2106  df-clel 2109  df-nfc 2242  df-ne 2281  df-v 2657  df-dif 3037  df-nul 3328 This theorem is referenced by:  neq0r  3341  opnzi  4115  elqsn0  6449  fin0  6729  infn0  6749  fsumcllem  11053  setsfun0  11831
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