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Theorem neq0r 3211
Description: An inhabited class is nonempty. See n0rf 3209 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 3210 . 2 (x x AA ≠ ∅)
21neneqd 2204 1 (x x A → ¬ A = ∅)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1228  wex 1363   wcel 1375  c0 3200
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 532  ax-in2 533  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1364  ax-ie2 1365  ax-8 1377  ax-10 1378  ax-11 1379  ax-i12 1380  ax-bnd 1381  ax-4 1382  ax-17 1401  ax-i9 1405  ax-ial 1410  ax-i5r 1411  ax-ext 2005
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-fal 1234  df-nf 1330  df-sb 1629  df-clab 2010  df-cleq 2016  df-clel 2019  df-nfc 2150  df-ne 2189  df-v 2536  df-dif 2896  df-nul 3201
This theorem is referenced by: (None)
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