Theorem df1o2 3111

Description: Expanded value of the ordinal number 1.

Assertion

Ref	Expression
df1o2	⊢ 1o = {∅}

Proof of Theorem df1o2

Step	Hyp	Ref	Expression
1		df-1o 3104	. 2 ⊢ 1o = suc ∅
2		df-suc 2205	. 2 ⊢ suc ∅ = (∅ ∪ {∅})
3		uncom 1604	. . 3 ⊢ (∅ ∪ {∅}) = ({∅} ∪ ∅)
4		un0 1721	. . 3 ⊢ ({∅} ∪ ∅) = {∅}
5	3, 4	eqtr 1119	. 2 ⊢ (∅ ∪ {∅}) = {∅}
6	1, 2, 5	3eqtr 1123	1 ⊢ 1o = {∅}

Syntax hints:   = wceq 1091   ∪ cun 1485  ∅c0 1707  {csn 1808  suc csuc 2201  1_oc1o 3099

This theorem is referenced by:  df2o2 3112  0ne1oOLD 3113  el1o 3115  oe0m1 3129  map0e 3266  map0 3268  ensn1 3329  en1 3331  map1 3335  cfsuc 3709  xp1en 3722  xp2cda 3723  infmap2 4953

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-dif 1489  df-un 1490  df-nul 1708  df-suc 2205  df-1o 3104

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