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Theorem nnnn0i 10799
Description: A positive integer 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 10798 . 2  |-  ( N  e.  NN  ->  N  e.  NN0 )
31, 2ax-mp 5 1  |-  N  e. 
NN0
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1767   NNcn 10532   NN0cn0 10791
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115  df-un 3481  df-in 3483  df-ss 3490  df-n0 10792
This theorem is referenced by:  1nn0  10807  2nn0  10808  3nn0  10809  4nn0  10810  5nn0  10811  6nn0  10812  7nn0  10813  8nn0  10814  9nn0  10815  10nn0  10816  numlt  10991  numlti  10996  faclbnd4lem1  12335  divalglem6  13911  pockthi  14280  dec5dvds2  14406  modxp1i  14411  mod2xnegi  14412  43prm  14461  83prm  14462  317prm  14465  strlemor2  14579  strlemor3  14580  log2ublem2  23006  ballotlemfmpn  28073  ballotth  28116
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