Theorem nn0rei 9187

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 9180	. 2 |- NN0 C_ RR
2		nn0re.1	. 2 |- A e. NN0
3	1, 2	sselii 3153	1 |- A e. RR

Syntax hints:   e. wcel 2148   RRcr 7810   NN0cn0 9176

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 4122  ax-cnex 7902  ax-resscn 7903  ax-1re 7905  ax-addrcl 7908  ax-rnegex 7920

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 2740  df-un 3134  df-in 3136  df-ss 3143  df-sn 3599  df-int 3846  df-inn 8920  df-n0 9177

This theorem is referenced by:  nn0cni  9188  nn0le2xi  9226  nn0lele2xi  9227  numlt  9408  numltc  9409  decle  9417  decleh  9418