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Theorem suc0 5984
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 5916 . 2 suc ∅ = (∅ ∪ {∅})
2 uncom 3921 . 2 (∅ ∪ {∅}) = ({∅} ∪ ∅)
3 un0 4131 . 2 ({∅} ∪ ∅) = {∅}
41, 2, 33eqtri 2791 1 suc ∅ = {∅}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1652  cun 3732  c0 4081  {csn 4336  suc csuc 5912
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-9 2164  ax-10 2183  ax-11 2198  ax-12 2211  ax-ext 2743
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 874  df-tru 1656  df-ex 1875  df-nf 1879  df-sb 2063  df-clab 2752  df-cleq 2758  df-clel 2761  df-nfc 2896  df-v 3352  df-dif 3737  df-un 3739  df-nul 4082  df-suc 5916
This theorem is referenced by:  df1o2  7781  axdc3lem4  9532
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