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Theorem suc0 6287
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 6219 . 2 suc ∅ = (∅ ∪ {∅})
2 uncom 4067 . 2 (∅ ∪ {∅}) = ({∅} ∪ ∅)
3 un0 4305 . 2 ({∅} ∪ ∅) = {∅}
41, 2, 33eqtri 2769 1 suc ∅ = {∅}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1543  cun 3864  c0 4237  {csn 4541  suc csuc 6215
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-ext 2708
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-tru 1546  df-fal 1556  df-ex 1788  df-sb 2071  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3410  df-dif 3869  df-un 3871  df-nul 4238  df-suc 6219
This theorem is referenced by:  df1o2  8214  axdc3lem4  10067
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