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Theorem nnex 8400
Description: The set of positive integers exists. (Contributed by NM, 3-Oct-1999.) (Revised by Mario Carneiro, 17-Nov-2014.)
Assertion
Ref Expression
nnex ℕ ∈ V

Proof of Theorem nnex
StepHypRef Expression
1 cnex 7445 . 2 ℂ ∈ V
2 nnsscn 8399 . 2 ℕ ⊆ ℂ
31, 2ssexi 3969 1 ℕ ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1438  Vcvv 2619  cc 7327  cn 8394
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-sep 3949  ax-cnex 7415  ax-resscn 7416  ax-1re 7418  ax-addrcl 7421
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-v 2621  df-in 3003  df-ss 3010  df-int 3684  df-inn 8395
This theorem is referenced by:  nn0ex  8649  nn0ennn  9805  climrecvg1n  10701  climcvg1nlem  10702  divcnv  10852  trireciplem  10855  expcnvap0  10857  expcnv  10859  geo2lim  10871  prmex  11188  qnumval  11256  qdenval  11257  oddennn  11298  evenennn  11299  xpnnen  11300  znnen  11304
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