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Theorem elni 8758
 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 8754 . . 3
21eleq2i 2502 . 2
3 eldifsn 3929 . 2
42, 3bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   wcel 1726   wne 2601   cdif 3319  c0 3630  csn 3816  com 4848  cnpi 8724 This theorem is referenced by:  elni2  8759  0npi  8764  1pi  8765  addclpi  8774  mulclpi  8775  nlt1pi  8788  indpi  8789 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-v 2960  df-dif 3325  df-sn 3822  df-ni 8754
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