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Theorem nnnn0i 10221
Description: A natural number is a nonnegative integer. (Contributed by NM, 20-Jun-2005.)
Hypothesis
Ref Expression
nnnn0.1  |-  N  e.  NN
Assertion
Ref Expression
nnnn0i  |-  N  e. 
NN0

Proof of Theorem nnnn0i
StepHypRef Expression
1 nnnn0.1 . 2  |-  N  e.  NN
2 nnnn0 10220 . 2  |-  ( N  e.  NN  ->  N  e.  NN0 )
31, 2ax-mp 8 1  |-  N  e. 
NN0
Colors of variables: wff set class
Syntax hints:    e. wcel 1725   NNcn 9992   NN0cn0 10213
This theorem is referenced by:  1nn0  10229  2nn0  10230  3nn0  10231  4nn0  10232  5nn0  10233  6nn0  10234  7nn0  10235  8nn0  10236  9nn0  10237  10nn0  10238  numlt  10393  numlti  10398  faclbnd4lem1  11576  divalglem6  12910  pockthi  13267  dec5dvds2  13393  modxp1i  13398  mod2xnegi  13399  43prm  13436  83prm  13437  317prm  13440  strlemor2  13549  strlemor3  13550  log2ublem2  20779  ballotlemfmpn  24744  ballotth  24787
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-un 3317  df-in 3319  df-ss 3326  df-n0 10214
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