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Theorem nn0rei 8192
 Description: A nonnegative integer is a real number. (Contributed by NM, 14-May-2003.)
Hypothesis
Ref Expression
nn0re.1
Assertion
Ref Expression
nn0rei

Proof of Theorem nn0rei
StepHypRef Expression
1 nn0ssre 8185 . 2
2 nn0re.1 . 2
31, 2sselii 2942 1
 Colors of variables: wff set class Syntax hints:   wcel 1393  cr 6888  cn0 8181 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-cnex 6975  ax-resscn 6976  ax-1re 6978  ax-addrcl 6981  ax-rnegex 6993 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-sn 3381  df-int 3616  df-inn 7915  df-n0 8182 This theorem is referenced by:  nn0cni  8193  nn0le2xi  8232  nn0lele2xi  8233  numlt  8386  numltc  8387
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