Theorem n0r 3371

Description: An inhabited class is nonempty. See n0rf 3370 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

Step	Hyp	Ref	Expression
1		nfcv 2279	. 2 |- F/_ x A
2	1	n0rf 3370	1 |- ( E. x x e. A -> A =/= (/) )

Syntax hints:   -> wi 4   E.wex 1468   e. wcel 1480   =/= wne 2306   (/)c0 3358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ne 2307  df-v 2683  df-dif 3068  df-nul 3359

This theorem is referenced by:  neq0r  3372  opnzi  4152  elqsn0  6491  fin0  6772  infn0  6792  fsumcllem  11161  setsfun0  11984