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Theorem n0i 3263
 Description: If a set has elements, it is not empty. A set with elements is also inhabited, see elex2 2616. (Contributed by NM, 31-Dec-1993.)
Assertion
Ref Expression
n0i

Proof of Theorem n0i
StepHypRef Expression
1 noel 3262 . . 3
2 eleq2 2143 . . 3
31, 2mtbiri 633 . 2
43con2i 590 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1285   wcel 1434  c0 3258 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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-dif 2976  df-nul 3259 This theorem is referenced by:  ne0i  3264  unidif0  3949  iin0r  3951  nnm00  6168  enq0tr  6686
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