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Theorem suc0 6459
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 6390 . 2 suc ∅ = (∅ ∪ {∅})
2 uncom 4158 . 2 (∅ ∪ {∅}) = ({∅} ∪ ∅)
3 un0 4394 . 2 ({∅} ∪ ∅) = {∅}
41, 2, 33eqtri 2769 1 suc ∅ = {∅}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  cun 3949  c0 4333  {csn 4626  suc csuc 6386
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-dif 3954  df-un 3956  df-nul 4334  df-suc 6390
This theorem is referenced by:  df1o2  8513  axdc3lem4  10493  pw2bday  28418
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