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Theorem suc0 5716
 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 5646 . 2 suc ∅ = (∅ ∪ {∅})
2 uncom 3719 . 2 (∅ ∪ {∅}) = ({∅} ∪ ∅)
3 un0 3919 . 2 ({∅} ∪ ∅) = {∅}
41, 2, 33eqtri 2636 1 suc ∅ = {∅}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475   ∪ cun 3538  ∅c0 3874  {csn 4125  suc csuc 5642 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-dif 3543  df-un 3545  df-nul 3875  df-suc 5646 This theorem is referenced by:  df1o2  7459  axdc3lem4  9158
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