Theorem nn0rei 9524

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 9517	. 2 |- NN0 C_ RR
2		nn0re.1	. 2 |- A e. NN0
3	1, 2	sselii 3239	1 |- A e. RR

Syntax hints:   e. wcel 2205   RRcr 8142   NN0cn0 9513

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 2216  ax-sep 4233  ax-cnex 8234  ax-resscn 8235  ax-1re 8237  ax-addrcl 8240  ax-rnegex 8252

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-ral 2527  df-rex 2528  df-v 2817  df-un 3218  df-in 3220  df-ss 3227  df-sn 3700  df-int 3955  df-inn 9255  df-n0 9514

This theorem is referenced by:  nn0cni  9525  nn0le2xi  9563  nn0lele2xi  9564  numlt  9751  numltc  9752  decle  9760  decleh  9761  modsubi  13142