Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  nn0rei Unicode version

Theorem nn0rei 9041
 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 9034 . 2
2 nn0re.1 . 2
31, 2sselii 3101 1
 Colors of variables: wff set class Syntax hints:   wcel 2112  cr 7672  cn0 9030 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2123  ax-sep 4056  ax-cnex 7764  ax-resscn 7765  ax-1re 7767  ax-addrcl 7770  ax-rnegex 7782 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1732  df-clab 2128  df-cleq 2134  df-clel 2137  df-nfc 2272  df-ral 2423  df-rex 2424  df-v 2693  df-un 3082  df-in 3084  df-ss 3091  df-sn 3540  df-int 3782  df-inn 8774  df-n0 9031 This theorem is referenced by:  nn0cni  9042  nn0le2xi  9080  nn0lele2xi  9081  numlt  9259  numltc  9260  decle  9268  decleh  9269
 Copyright terms: Public domain W3C validator