Theorem nn0rei 9254

Description: A nonnegative integer is a real number. (Contributed by NM, 14-May-2003.)

Hypothesis

Ref	Expression
nn0re.1	|- A e. NN0

Assertion

Ref	Expression
nn0rei	|- A e. RR

Proof of Theorem nn0rei

Step	Hyp	Ref	Expression
1		nn0ssre 9247	. 2 |- NN0 C_ RR
2		nn0re.1	. 2 |- A e. NN0
3	1, 2	sselii 3177	1 |- A e. RR

Syntax hints:   e. wcel 2164   RRcr 7873   NN0cn0 9243

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175  ax-sep 4148  ax-cnex 7965  ax-resscn 7966  ax-1re 7968  ax-addrcl 7971  ax-rnegex 7983

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-ral 2477  df-rex 2478  df-v 2762  df-un 3158  df-in 3160  df-ss 3167  df-sn 3625  df-int 3872  df-inn 8985  df-n0 9244

This theorem is referenced by:  nn0cni  9255  nn0le2xi  9293  nn0lele2xi  9294  numlt  9475  numltc  9476  decle  9484  decleh  9485