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Theorem niex 7021
Description: The class of positive integers is a set. (Contributed by NM, 15-Aug-1995.)
Assertion
Ref Expression
niex N ∈ V

Proof of Theorem niex
StepHypRef Expression
1 omex 4445 . 2 ω ∈ V
2 df-ni 7013 . . 3 N = (ω ∖ {∅})
3 difss 3149 . . 3 (ω ∖ {∅}) ⊆ ω
42, 3eqsstri 3079 . 2 N ⊆ ω
51, 4ssexi 4006 1 N ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1448  Vcvv 2641  cdif 3018  c0 3310  {csn 3474  ωcom 4442  Ncnpi 6981
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 584  ax-in2 585  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082  ax-sep 3986  ax-iinf 4440
This theorem depends on definitions:  df-bi 116  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-ral 2380  df-v 2643  df-dif 3023  df-in 3027  df-ss 3034  df-int 3719  df-iom 4443  df-ni 7013
This theorem is referenced by:  enqex  7069  nqex  7072  enq0ex  7148  nq0ex  7149
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