Theorem nn0rei 9503

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 9496	. 2 ⊢ ℕ0 ⊆ ℝ
2		nn0re.1	. 2 ⊢ 𝐴 ∈ ℕ0
3	1, 2	sselii 3234	1 ⊢ 𝐴 ∈ ℝ

Syntax hints:   ∈ wcel 2203  ℝcr 8122  ℕ₀cn0 9492

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214  ax-sep 4227  ax-cnex 8214  ax-resscn 8215  ax-1re 8217  ax-addrcl 8220  ax-rnegex 8232

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-ral 2525  df-rex 2526  df-v 2814  df-un 3214  df-in 3216  df-ss 3223  df-sn 3694  df-int 3949  df-inn 9234  df-n0 9493

This theorem is referenced by:  nn0cni  9504  nn0le2xi  9542  nn0lele2xi  9543  numlt  9729  numltc  9730  decle  9738  decleh  9739  modsubi  13110