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Theorem suc0 5960
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 5890 . 2 suc ∅ = (∅ ∪ {∅})
2 uncom 3900 . 2 (∅ ∪ {∅}) = ({∅} ∪ ∅)
3 un0 4110 . 2 ({∅} ∪ ∅) = {∅}
41, 2, 33eqtri 2786 1 suc ∅ = {∅}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1632  cun 3713  c0 4058  {csn 4321  suc csuc 5886
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-v 3342  df-dif 3718  df-un 3720  df-nul 4059  df-suc 5890
This theorem is referenced by:  df1o2  7741  axdc3lem4  9467
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