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Theorem suc0 4148
 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 4108 . 2 suc ∅ = (∅ ∪ {∅})
2 uncom 3087 . 2 (∅ ∪ {∅}) = ({∅} ∪ ∅)
3 un0 3251 . 2 ({∅} ∪ ∅) = {∅}
41, 2, 33eqtri 2064 1 suc ∅ = {∅}
 Colors of variables: wff set class Syntax hints:   = wceq 1243   ∪ cun 2915  ∅c0 3224  {csn 3375  suc csuc 4102 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 2559  df-dif 2920  df-un 2922  df-nul 3225  df-suc 4108 This theorem is referenced by:  ordtriexmidlem  4245  ordtri2orexmid  4248  2ordpr  4249  onsucsssucexmid  4252  onsucelsucexmid  4255  ordsoexmid  4286  ordtri2or2exmid  4296  nnregexmid  4342  tfr0  5937  df1o2  6013
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