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Theorem n0r 3346
Description: An inhabited class is nonempty. See n0rf 3345 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 2258 . 2 𝑥𝐴
21n0rf 3345 1 (∃𝑥 𝑥𝐴𝐴 ≠ ∅)
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1453  wcel 1465  wne 2285  c0 3333
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-fal 1322  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-ne 2286  df-v 2662  df-dif 3043  df-nul 3334
This theorem is referenced by:  neq0r  3347  opnzi  4127  elqsn0  6466  fin0  6747  infn0  6767  fsumcllem  11136  setsfun0  11922
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