Theorem nn0rei 9146

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 9139	. 2 |- NN0 C_ RR
2		nn0re.1	. 2 |- A e. NN0
3	1, 2	sselii 3144	1 |- A e. RR

Syntax hints:   e. wcel 2141   RRcr 7773   NN0cn0 9135

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152  ax-sep 4107  ax-cnex 7865  ax-resscn 7866  ax-1re 7868  ax-addrcl 7871  ax-rnegex 7883

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-ral 2453  df-rex 2454  df-v 2732  df-un 3125  df-in 3127  df-ss 3134  df-sn 3589  df-int 3832  df-inn 8879  df-n0 9136

This theorem is referenced by:  nn0cni  9147  nn0le2xi  9185  nn0lele2xi  9186  numlt  9367  numltc  9368  decle  9376  decleh  9377