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Theorem nn0rei 8956
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 8949 . 2 0 ⊆ ℝ
2 nn0re.1 . 2 𝐴 ∈ ℕ0
31, 2sselii 3064 1 𝐴 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 1465  cr 7587  0cn0 8945
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-sep 4016  ax-cnex 7679  ax-resscn 7680  ax-1re 7682  ax-addrcl 7685  ax-rnegex 7697
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-ral 2398  df-rex 2399  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-sn 3503  df-int 3742  df-inn 8689  df-n0 8946
This theorem is referenced by:  nn0cni  8957  nn0le2xi  8995  nn0lele2xi  8996  numlt  9174  numltc  9175  decle  9183  decleh  9184
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