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Theorem nnex 8366
Description: The set of positive integers exists. (Contributed by NM, 3-Oct-1999.) (Revised by Mario Carneiro, 17-Nov-2014.)
Assertion
Ref Expression
nnex  |-  NN  e.  _V

Proof of Theorem nnex
StepHypRef Expression
1 cnex 7413 . 2  |-  CC  e.  _V
2 nnsscn 8365 . 2  |-  NN  C_  CC
31, 2ssexi 3954 1  |-  NN  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1436   _Vcvv 2615   CCcc 7295   NNcn 8360
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-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  ax-sep 3934  ax-cnex 7383  ax-resscn 7384  ax-1re 7386  ax-addrcl 7389
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-ral 2360  df-v 2617  df-in 2994  df-ss 3001  df-int 3674  df-inn 8361
This theorem is referenced by:  nn0ex  8615  nn0ennn  9771  climrecvg1n  10651  climcvg1nlem  10652  prmex  11020  qnumval  11088  qdenval  11089  oddennn  11130  evenennn  11131  xpnnen  11132  znnen  11136
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