ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  0nn0 GIF version

Theorem 0nn0 8064
Description: 0 is a nonnegative integer. (Contributed by Raph Levien, 10-Dec-2002.)
Assertion
Ref Expression
0nn0 0 0

Proof of Theorem 0nn0
StepHypRef Expression
1 eqid 2040 . 2 0 = 0
2 elnn0 8051 . . . 4 (0 0 ↔ (0 0 = 0))
32biimpri 124 . . 3 ((0 0 = 0) → 0 0)
43olcs 655 . 2 (0 = 0 → 0 0)
51, 4ax-mp 7 1 0 0
Colors of variables: wff set class
Syntax hints:   wo 629   = wceq 1243   wcel 1393  0cc0 6779  cn 7787  0cn0 8049
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-1cn 6867  ax-icn 6869  ax-addcl 6870  ax-mulcl 6872  ax-i2m1 6879
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-v 2556  df-un 2919  df-sn 3376  df-n0 8050
This theorem is referenced by:  elnn0z  8126  nn0ind-raph  8223  numlti  8259  nummul1c  8271  decaddc2  8278  decaddi  8279  decaddci  8280  decaddci2  8281  6p5e11  8285  7p4e11  8287  8p3e11  8291  9p2e11  8297  10p10e20  8305  0elfz  8839  4fvwrd4  8859  exple1  9057  nn0seqcvgd  9327  ialgcvg  9334
  Copyright terms: Public domain W3C validator