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Theorem suc0 4117
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 4077 . 2 suc ∅ = (∅ ∪ {∅})
2 uncom 3084 . 2 (∅ ∪ {∅}) = ({∅} ∪ ∅)
3 un0 3248 . 2 ({∅} ∪ ∅) = {∅}
41, 2, 33eqtri 2064 1 suc ∅ = {∅}
Colors of variables: wff set class
Syntax hints:   = wceq 1243  cun 2912  c0 3221  {csn 3370  suc csuc 4071
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-in1 544  ax-in2 545  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
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-dif 2917  df-un 2919  df-nul 3222  df-suc 4077
This theorem is referenced by:  ordtriexmidlem  4211  ordtri2orexmid  4214  onsucsssucexmid  4215  onsucelsucexmidlem  4217  onsucelsucexmid  4218  ordsoexmid  4243  nnregexmid  4288  tfr0  5882  df1o2  5956
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