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Theorem neq0r 3229
 Description: An inhabited class is nonempty. See n0rf 3227 for more discussion. (Contributed by Jim Kingdon, 31-Jul-2018.)
Assertion
Ref Expression
neq0r (x x A → ¬ A = ∅)
Distinct variable group:   x,A

Proof of Theorem neq0r
StepHypRef Expression
1 n0r 3228 . 2 (x x AA ≠ ∅)
21neneqd 2221 1 (x x A → ¬ A = ∅)
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   = wceq 1242  ∃wex 1378   ∈ wcel 1390  ∅c0 3218 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ne 2203  df-v 2553  df-dif 2914  df-nul 3219 This theorem is referenced by:  fzn  8676
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