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Theorem pinn 9277
Description: A positive integer is a natural number. (Contributed by NM, 15-Aug-1995.) (New usage is discouraged.)
Assertion
Ref Expression
pinn

Proof of Theorem pinn
StepHypRef Expression
1 df-ni 9271 . . 3
2 difss 3630 . . 3
31, 2eqsstri 3533 . 2
43sseli 3499 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  e.wcel 1818  \cdif 3472   c0 3784  {csn 4029   com 6700   cnpi 9243
This theorem is referenced by:  pion  9278  piord  9279  mulidpi  9285  addclpi  9291  mulclpi  9292  addcompi  9293  addasspi  9294  mulcompi  9295  mulasspi  9296  distrpi  9297  addcanpi  9298  mulcanpi  9299  addnidpi  9300  ltexpi  9301  ltapi  9302  ltmpi  9303  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-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-ni 9271
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