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

Theorem nn0sscn 8732
Description: Nonnegative integers are a subset of the complex numbers.) (Contributed by NM, 9-May-2004.)
Assertion
Ref Expression
nn0sscn 0 ⊆ ℂ

Proof of Theorem nn0sscn
StepHypRef Expression
1 nn0ssre 8731 . 2 0 ⊆ ℝ
2 ax-resscn 7491 . 2 ℝ ⊆ ℂ
31, 2sstri 3035 1 0 ⊆ ℂ
Colors of variables: wff set class
Syntax hints:  wss 3000  cc 7402  cr 7403  0cn0 8727
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071  ax-sep 3963  ax-cnex 7490  ax-resscn 7491  ax-1re 7493  ax-addrcl 7496  ax-rnegex 7508
This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-ral 2365  df-rex 2366  df-v 2622  df-un 3004  df-in 3006  df-ss 3013  df-sn 3456  df-int 3695  df-inn 8477  df-n0 8728
This theorem is referenced by:  nn0cn  8737  nn0expcl  10023  fsumnn0cl  10851
  Copyright terms: Public domain W3C validator