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Theorem suc0 4394
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 4354 . 2 suc ∅ = (∅ ∪ {∅})
2 uncom 3271 . 2 (∅ ∪ {∅}) = ({∅} ∪ ∅)
3 un0 3447 . 2 ({∅} ∪ ∅) = {∅}
41, 2, 33eqtri 2195 1 suc ∅ = {∅}
Colors of variables: wff set class
Syntax hints:   = wceq 1348  cun 3119  c0 3414  {csn 3581  suc csuc 4348
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 609  ax-in2 610  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-dif 3123  df-un 3125  df-nul 3415  df-suc 4354
This theorem is referenced by:  ordtriexmidlem  4501  ordtri2orexmid  4505  2ordpr  4506  onsucsssucexmid  4509  onsucelsucexmid  4512  ordsoexmid  4544  ordtri2or2exmid  4553  ontri2orexmidim  4554  nnregexmid  4603  omsinds  4604  tfr0dm  6298  df1o2  6405  nninfsellemdc  13965
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