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Theorem nn0rei 8682
Description: A nonnegative integer is a real number. (Contributed by NM, 14-May-2003.)
Hypothesis
Ref Expression
nn0re.1 𝐴 ∈ ℕ0
Assertion
Ref Expression
nn0rei 𝐴 ∈ ℝ

Proof of Theorem nn0rei
StepHypRef Expression
1 nn0ssre 8675 . 2 0 ⊆ ℝ
2 nn0re.1 . 2 𝐴 ∈ ℕ0
31, 2sselii 3022 1 𝐴 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 1438  cr 7347  0cn0 8671
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-sep 3957  ax-cnex 7434  ax-resscn 7435  ax-1re 7437  ax-addrcl 7440  ax-rnegex 7452
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-rex 2365  df-v 2621  df-un 3003  df-in 3005  df-ss 3012  df-sn 3452  df-int 3689  df-inn 8421  df-n0 8672
This theorem is referenced by:  nn0cni  8683  nn0le2xi  8721  nn0lele2xi  8722  numlt  8899  numltc  8900  decle  8908  decleh  8909
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