ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  niex GIF version

Theorem niex 6438
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 4341 . 2 ω ∈ V
2 df-ni 6430 . . 3 N = (ω ∖ {∅})
3 difss 3095 . . 3 (ω ∖ {∅}) ⊆ ω
42, 3eqsstri 3000 . 2 N ⊆ ω
51, 4ssexi 3920 1 N ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1407  Vcvv 2572  cdif 2939  c0 3249  {csn 3400  ωcom 4338  Ncnpi 6398
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 552  ax-in2 553  ax-io 638  ax-5 1350  ax-7 1351  ax-gen 1352  ax-ie1 1396  ax-ie2 1397  ax-8 1409  ax-10 1410  ax-11 1411  ax-i12 1412  ax-bndl 1413  ax-4 1414  ax-17 1433  ax-i9 1437  ax-ial 1441  ax-i5r 1442  ax-ext 2036  ax-sep 3900  ax-iinf 4336
This theorem depends on definitions:  df-bi 114  df-tru 1260  df-nf 1364  df-sb 1660  df-clab 2041  df-cleq 2047  df-clel 2050  df-nfc 2181  df-ral 2326  df-v 2574  df-dif 2945  df-in 2949  df-ss 2956  df-int 3641  df-iom 4339  df-ni 6430
This theorem is referenced by:  enqex  6486  nqex  6489  enq0ex  6565  nq0ex  6566
  Copyright terms: Public domain W3C validator