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Theorem suc0 4093
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 4053 . 2 suc ∅ = (∅ ∪ {∅})
2 uncom 3060 . 2 (∅ ∪ {∅}) = ({∅} ∪ ∅)
3 un0 3224 . 2 ({∅} ∪ ∅) = {∅}
41, 2, 33eqtri 2042 1 suc ∅ = {∅}
Colors of variables: wff set class
Syntax hints:   = wceq 1226  cun 2888  c0 3197  {csn 3346  suc csuc 4047
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 532  ax-in2 533  ax-io 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-v 2533  df-dif 2893  df-un 2895  df-nul 3198  df-suc 4053
This theorem is referenced by:  ordtriexmidlem  4188  ordtri2orexmid  4191  onsucsssucexmid  4192  onsucelsucexmidlem  4194  onsucelsucexmid  4195  ordsoexmid  4220  nnregexmid  4265  df1o2  5924
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