Theorem n0r 3485

Description: An inhabited class is nonempty. See n0rf 3484 for more discussion. (Contributed by Jim Kingdon, 31-Jul-2018.)

Assertion

Ref	Expression
n0r	⊢ (∃𝑥 𝑥 ∈ 𝐴 → 𝐴 ≠ ∅)

Distinct variable group:   𝑥,𝐴

Proof of Theorem n0r

Step	Hyp	Ref	Expression
1		nfcv 2352	. 2 ⊢ Ⅎ𝑥𝐴
2	1	n0rf 3484	1 ⊢ (∃𝑥 𝑥 ∈ 𝐴 → 𝐴 ≠ ∅)

Syntax hints:   → wi 4  ∃wex 1518   ∈ wcel 2180   ≠ wne 2380  ∅c0 3471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 617  ax-in2 618  ax-io 713  ax-5 1473  ax-7 1474  ax-gen 1475  ax-ie1 1519  ax-ie2 1520  ax-8 1530  ax-10 1531  ax-11 1532  ax-i12 1533  ax-bndl 1535  ax-4 1536  ax-17 1552  ax-i9 1556  ax-ial 1560  ax-i5r 1561  ax-ext 2191

This theorem depends on definitions:  df-bi 117  df-tru 1378  df-fal 1381  df-nf 1487  df-sb 1789  df-clab 2196  df-cleq 2202  df-clel 2205  df-nfc 2341  df-ne 2381  df-v 2781  df-dif 3179  df-nul 3472

This theorem is referenced by:  neq0r  3486  opnzi  4300  elqsn0  6721  fin0  7015  infn0  7035  fiubm  11017  lswex  11089  fsumcllem  11876  fprodcllem  12083  setsfun0  13034  gsumwsubmcl  13495  gsumwmhm  13497