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Theorem nn0rei 9189
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 9182 . 2 0 ⊆ ℝ
2 nn0re.1 . 2 𝐴 ∈ ℕ0
31, 2sselii 3154 1 𝐴 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 2148  cr 7812  0cn0 9178
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-sep 4123  ax-cnex 7904  ax-resscn 7905  ax-1re 7907  ax-addrcl 7910  ax-rnegex 7922
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-ral 2460  df-rex 2461  df-v 2741  df-un 3135  df-in 3137  df-ss 3144  df-sn 3600  df-int 3847  df-inn 8922  df-n0 9179
This theorem is referenced by:  nn0cni  9190  nn0le2xi  9228  nn0lele2xi  9229  numlt  9410  numltc  9411  decle  9419  decleh  9420
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