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Theorem ne0i 3207
Description: If a set has elements, it is not empty. A set with elements is also inhabited, see elex2 2547. (Contributed by NM, 31-Dec-1993.)
Assertion
Ref Expression
ne0i  =/=  (/)

Proof of Theorem ne0i
StepHypRef Expression
1 n0i 3206 . 2  (/)
21neneqad 2262 1  =/=  (/)
Colors of variables: wff set class
Syntax hints:   wi 4   wcel 1374    =/= wne 2186   (/)c0 3201
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 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-ne 2188  df-v 2537  df-dif 2897  df-nul 3202
This theorem is referenced by:  vn0  3208  inelcm  3259  rzal  3297  rexn0  3298  snnzg  3459  prnz  3464  tpnz  3467  onn0  4086  nn0eln0  4268  ordge1n0im  5934  nnmord  6001  addclpi  6187  mulclpi  6188
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