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Theorem elni 6406
 Description: Membership in the class of positive integers. (Contributed by NM, 15-Aug-1995.)
Assertion
Ref Expression
elni

Proof of Theorem elni
StepHypRef Expression
1 df-ni 6402 . . 3
21eleq2i 2104 . 2
3 eldifsn 3495 . 2
42, 3bitri 173 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98   wcel 1393   wne 2204   cdif 2914  c0 3224  csn 3375  com 4313  cnpi 6370 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ne 2206  df-v 2559  df-dif 2920  df-sn 3381  df-ni 6402 This theorem is referenced by:  0npi  6411  elni2  6412  1pi  6413  addclpi  6425  mulclpi  6426  nlt1pig  6439  indpi  6440  nqnq0pi  6536  prarloclemcalc  6600
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