Theorem nn0rei 9181

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

Step	Hyp	Ref	Expression
1		nn0ssre 9174	. 2 ⊢ ℕ0 ⊆ ℝ
2		nn0re.1	. 2 ⊢ 𝐴 ∈ ℕ0
3	1, 2	sselii 3152	1 ⊢ 𝐴 ∈ ℝ

Syntax hints:   ∈ wcel 2148  ℝcr 7805  ℕ₀cn0 9170

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 4119  ax-cnex 7897  ax-resscn 7898  ax-1re 7900  ax-addrcl 7903  ax-rnegex 7915

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 3844  df-inn 8914  df-n0 9171

This theorem is referenced by:  nn0cni  9182  nn0le2xi  9220  nn0lele2xi  9221  numlt  9402  numltc  9403  decle  9411  decleh  9412