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Theorem elni 6292
Description: Membership in the class of positive integers. (Contributed by NM, 15-Aug-1995.)
Assertion
Ref Expression
elni  N.  om  =/=  (/)

Proof of Theorem elni
StepHypRef Expression
1 df-ni 6288 . . 3  N.  om  \  { (/) }
21eleq2i 2101 . 2  N.  om  \  { (/) }
3 eldifsn 3486 . 2  om  \  { (/)
}  om  =/=  (/)
42, 3bitri 173 1  N.  om  =/=  (/)
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98   wcel 1390    =/= wne 2201    \ cdif 2908   (/)c0 3218   {csn 3367   omcom 4256   N.cnpi 6256
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ne 2203  df-v 2553  df-dif 2914  df-sn 3373  df-ni 6288
This theorem is referenced by:  0npi  6297  elni2  6298  1pi  6299  addclpi  6311  mulclpi  6312  nlt1pig  6325  indpi  6326  nqnq0pi  6421  prarloclemcalc  6485
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