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Theorem nnex 8683
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 7708 . 2 ℂ ∈ V
2 nnsscn 8682 . 2 ℕ ⊆ ℂ
31, 2ssexi 4034 1 ℕ ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1463  Vcvv 2658  cc 7582  cn 8677
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-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-sep 4014  ax-cnex 7675  ax-resscn 7676  ax-1re 7678  ax-addrcl 7681
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-ral 2396  df-v 2660  df-in 3045  df-ss 3052  df-int 3740  df-inn 8678
This theorem is referenced by:  nn0ex  8934  nn0ennn  10146  climrecvg1n  11057  climcvg1nlem  11058  divcnv  11206  trireciplem  11209  expcnvap0  11211  expcnv  11213  geo2lim  11225  prmex  11690  qnumval  11758  qdenval  11759  oddennn  11800  evenennn  11801  xpnnen  11802  znnen  11806  qnnen  11839  ndxarg  11877  trilpo  13038
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