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Theorem suc0 6234
 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 6166 . 2 suc ∅ = (∅ ∪ {∅})
2 uncom 4080 . 2 (∅ ∪ {∅}) = ({∅} ∪ ∅)
3 un0 4298 . 2 ({∅} ∪ ∅) = {∅}
41, 2, 33eqtri 2825 1 suc ∅ = {∅}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538   ∪ cun 3879  ∅c0 4243  {csn 4525  suc csuc 6162 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-dif 3884  df-un 3886  df-nul 4244  df-suc 6166 This theorem is referenced by:  df1o2  8102  axdc3lem4  9867
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