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Theorem nn0rei 9186
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 9179 . 2 0 ⊆ ℝ
2 nn0re.1 . 2 𝐴 ∈ ℕ0
31, 2sselii 3152 1 𝐴 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 2148  cr 7809  0cn0 9175
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 4121  ax-cnex 7901  ax-resscn 7902  ax-1re 7904  ax-addrcl 7907  ax-rnegex 7919
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 2739  df-un 3133  df-in 3135  df-ss 3142  df-sn 3598  df-int 3845  df-inn 8919  df-n0 9176
This theorem is referenced by:  nn0cni  9187  nn0le2xi  9225  nn0lele2xi  9226  numlt  9407  numltc  9408  decle  9416  decleh  9417
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