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Theorem elni 9275
Description: Membership in the class of positive integers. (Contributed by NM, 15-Aug-1995.) (New usage is discouraged.)
Assertion
Ref Expression
elni

Proof of Theorem elni
StepHypRef Expression
1 df-ni 9271 . . 3
21eleq2i 2535 . 2
3 eldifsn 4155 . 2
42, 3bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  e.wcel 1818  =/=wne 2652  \cdif 3472   c0 3784  {csn 4029   com 6700   cnpi 9243
This theorem is referenced by:  elni2  9276  0npi  9281  1pi  9282  addclpi  9291  mulclpi  9292  nlt1pi  9305  indpi  9306
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-sn 4030  df-ni 9271
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