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Theorem n0r 3285
Description: An inhabited class is nonempty. See n0rf 3284 for more discussion. (Contributed by Jim Kingdon, 31-Jul-2018.)
Assertion
Ref Expression
n0r  |-  ( E. x  x  e.  A  ->  A  =/=  (/) )
Distinct variable group:    x, A

Proof of Theorem n0r
StepHypRef Expression
1 nfcv 2225 . 2  |-  F/_ x A
21n0rf 3284 1  |-  ( E. x  x  e.  A  ->  A  =/=  (/) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1424    e. wcel 1436    =/= wne 2251   (/)c0 3275
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-fal 1293  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-ne 2252  df-v 2617  df-dif 2990  df-nul 3276
This theorem is referenced by:  neq0r  3286  opnzi  4034  elqsn0  6306  fin0  6546  infn0  6566
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