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Theorem suc0 6258
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 6190 . 2 suc ∅ = (∅ ∪ {∅})
2 uncom 4126 . 2 (∅ ∪ {∅}) = ({∅} ∪ ∅)
3 un0 4341 . 2 ({∅} ∪ ∅) = {∅}
41, 2, 33eqtri 2845 1 suc ∅ = {∅}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1528  cun 3931  c0 4288  {csn 4557  suc csuc 6186
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-v 3494  df-dif 3936  df-un 3938  df-nul 4289  df-suc 6190
This theorem is referenced by:  df1o2  8105  axdc3lem4  9863
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