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Theorem niex 6553
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 4336 . 2 ω ∈ V
2 df-ni 6545 . . 3 N = (ω ∖ {∅})
3 difss 3099 . . 3 (ω ∖ {∅}) ⊆ ω
42, 3eqsstri 3030 . 2 N ⊆ ω
51, 4ssexi 3918 1 N ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1434  Vcvv 2602  cdif 2971  c0 3252  {csn 3400  ωcom 4333  Ncnpi 6513
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  ax-sep 3898  ax-iinf 4331
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-ral 2354  df-v 2604  df-dif 2976  df-in 2980  df-ss 2987  df-int 3639  df-iom 4334  df-ni 6545
This theorem is referenced by:  enqex  6601  nqex  6604  enq0ex  6680  nq0ex  6681
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