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Theorem nnnn0i 8363
Description: A positive integer is a nonnegative integer. (Contributed by NM, 20-Jun-2005.)
Hypothesis
Ref Expression
nnnn0.1 𝑁 ∈ ℕ
Assertion
Ref Expression
nnnn0i 𝑁 ∈ ℕ0

Proof of Theorem nnnn0i
StepHypRef Expression
1 nnnn0.1 . 2 𝑁 ∈ ℕ
2 nnnn0 8362 . 2 (𝑁 ∈ ℕ → 𝑁 ∈ ℕ0)
31, 2ax-mp 7 1 𝑁 ∈ ℕ0
Colors of variables: wff set class
Syntax hints:  wcel 1434  cn 8106  0cn0 8355
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-n0 8356
This theorem is referenced by:  1nn0  8371  2nn0  8372  3nn0  8373  4nn0  8374  5nn0  8375  6nn0  8376  7nn0  8377  8nn0  8378  9nn0  8379  numlt  8582  declei  8593  numlti  8594
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