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Theorem suc0 4205
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 4165 . 2 suc ∅ = (∅ ∪ {∅})
2 uncom 3130 . 2 (∅ ∪ {∅}) = ({∅} ∪ ∅)
3 un0 3302 . 2 ({∅} ∪ ∅) = {∅}
41, 2, 33eqtri 2109 1 suc ∅ = {∅}
Colors of variables: wff set class
Syntax hints:   = wceq 1287  cun 2984  c0 3272  {csn 3425  suc csuc 4159
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2616  df-dif 2988  df-un 2990  df-nul 3273  df-suc 4165
This theorem is referenced by:  ordtriexmidlem  4302  ordtri2orexmid  4305  2ordpr  4306  onsucsssucexmid  4309  onsucelsucexmid  4312  ordsoexmid  4344  ordtri2or2exmid  4353  nnregexmid  4400  omsinds  4401  tfr0dm  6022  df1o2  6129  nninfsellemdc  11258
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