ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nn0sscn Unicode version

Theorem nn0sscn 9095
Description: Nonnegative integers are a subset of the complex numbers.) (Contributed by NM, 9-May-2004.)
Assertion
Ref Expression
nn0sscn  |-  NN0  C_  CC

Proof of Theorem nn0sscn
StepHypRef Expression
1 nn0ssre 9094 . 2  |-  NN0  C_  RR
2 ax-resscn 7824 . 2  |-  RR  C_  CC
31, 2sstri 3137 1  |-  NN0  C_  CC
Colors of variables: wff set class
Syntax hints:    C_ wss 3102   CCcc 7730   RRcr 7731   NN0cn0 9090
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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139  ax-sep 4082  ax-cnex 7823  ax-resscn 7824  ax-1re 7826  ax-addrcl 7829  ax-rnegex 7841
This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-rex 2441  df-v 2714  df-un 3106  df-in 3108  df-ss 3115  df-sn 3566  df-int 3808  df-inn 8834  df-n0 9091
This theorem is referenced by:  nn0cn  9100  nn0expcl  10433  fsumnn0cl  11300  fprodnn0cl  11509  eulerthlemrprm  12103  eulerthlema  12104
  Copyright terms: Public domain W3C validator