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Theorem pinn 8760
Description: A positive integer is a natural number. (Contributed by NM, 15-Aug-1995.) (New usage is discouraged.)
Assertion
Ref Expression
pinn  |-  ( A  e.  N.  ->  A  e.  om )

Proof of Theorem pinn
StepHypRef Expression
1 df-ni 8754 . . 3  |-  N.  =  ( om  \  { (/) } )
2 difss 3476 . . 3  |-  ( om 
\  { (/) } ) 
C_  om
31, 2eqsstri 3380 . 2  |-  N.  C_  om
43sseli 3346 1  |-  ( A  e.  N.  ->  A  e.  om )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1726    \ cdif 3319   (/)c0 3630   {csn 3816   omcom 4848   N.cnpi 8724
This theorem is referenced by:  pion  8761  piord  8762  mulidpi  8768  addclpi  8774  mulclpi  8775  addcompi  8776  addasspi  8777  mulcompi  8778  mulasspi  8779  distrpi  8780  addcanpi  8781  mulcanpi  8782  addnidpi  8783  ltexpi  8784  ltapi  8785  ltmpi  8786  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-v 2960  df-dif 3325  df-in 3329  df-ss 3336  df-ni 8754
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