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Theorem nnnn0i 11177
 Description: A positive integer is a nonnegative integer. (Contributed by NM, 20-Jun-2005.)
Hypothesis
Ref Expression
nnnn0i.1 𝑁 ∈ ℕ
Assertion
Ref Expression
nnnn0i 𝑁 ∈ ℕ0

Proof of Theorem nnnn0i
StepHypRef Expression
1 nnnn0i.1 . 2 𝑁 ∈ ℕ
2 nnnn0 11176 . 2 (𝑁 ∈ ℕ → 𝑁 ∈ ℕ0)
31, 2ax-mp 5 1 𝑁 ∈ ℕ0
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1977  ℕcn 10897  ℕ0cn0 11169 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-in 3547  df-ss 3554  df-n0 11170 This theorem is referenced by:  1nn0  11185  2nn0  11186  3nn0  11187  4nn0  11188  5nn0  11189  6nn0  11190  7nn0  11191  8nn0  11192  9nn0  11193  10nn0OLD  11194  numlt  11403  declei  11418  numlti  11421  faclbnd4lem1  12942  divalglem6  14959  pockthi  15449  dec5dvds2  15607  modxp1i  15612  mod2xnegi  15613  43prm  15667  83prm  15668  317prm  15671  strlemor2  15797  strlemor3  15798  log2ublem2  24474  ballotlemfmpn  29883  ballotth  29926  tgblthelfgott  40229  tgoldbach  40232  bgoldbachltOLD  40234  tgblthelfgottOLD  40236  tgoldbachOLD  40239
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