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Theorem suc0 4429
Description: The successor of the empty set. (Contributed by NM, 1-Feb-2005.)
Assertion
Ref Expression
suc0 suc ∅ = {∅}

Proof of Theorem suc0
StepHypRef Expression
1 df-suc 4389 . 2 suc ∅ = (∅ ∪ {∅})
2 uncom 3294 . 2 (∅ ∪ {∅}) = ({∅} ∪ ∅)
3 un0 3471 . 2 ({∅} ∪ ∅) = {∅}
41, 2, 33eqtri 2214 1 suc ∅ = {∅}
Colors of variables: wff set class
Syntax hints:   = wceq 1364  cun 3142  c0 3437  {csn 3607  suc csuc 4383
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-dif 3146  df-un 3148  df-nul 3438  df-suc 4389
This theorem is referenced by:  ordtriexmidlem  4536  ordtri2orexmid  4540  2ordpr  4541  onsucsssucexmid  4544  onsucelsucexmid  4547  ordsoexmid  4579  ordtri2or2exmid  4588  ontri2orexmidim  4589  nnregexmid  4638  omsinds  4639  tfr0dm  6346  df1o2  6453  nninfsellemdc  15213
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