Theorem n0r 3507

Description: An inhabited class is nonempty. See n0rf 3506 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 2373	. 2 ⊢ Ⅎ𝑥𝐴
2	1	n0rf 3506	1 ⊢ (∃𝑥 𝑥 ∈ 𝐴 → 𝐴 ≠ ∅)

Syntax hints:   → wi 4  ∃wex 1540   ∈ wcel 2201   ≠ wne 2401  ∅c0 3493

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 619  ax-in2 620  ax-io 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2212

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-fal 1403  df-nf 1509  df-sb 1810  df-clab 2217  df-cleq 2223  df-clel 2226  df-nfc 2362  df-ne 2402  df-v 2803  df-dif 3201  df-nul 3494

This theorem is referenced by:  neq0r  3508  opnzi  4329  elqsn0  6778  fin0  7079  infn0  7102  fiubm  11098  lswex  11174  fsumcllem  11983  fprodcllem  12190  setsfun0  13141  gsumwsubmcl  13602  gsumwmhm  13604  g0wlk0  16250