Theorem df2o2 6038

Description: Expanded value of the ordinal number 2. (Contributed by NM, 29-Jan-2004.)

Assertion

Ref	Expression
df2o2	⊢ 2𝑜 = {∅, {∅}}

Proof of Theorem df2o2

Step	Hyp	Ref	Expression
1		df2o3 6037	. 2 ⊢ 2𝑜 = {∅, 1𝑜}
2		df1o2 6036	. . 3 ⊢ 1𝑜 = {∅}
3	2	preq2i 3473	. 2 ⊢ {∅, 1𝑜} = {∅, {∅}}
4	1, 3	eqtri 2101	1 ⊢ 2𝑜 = {∅, {∅}}

Syntax hints:   = wceq 1284  ∅c0 3251  {csn 3398  {cpr 3399  1_𝑜c1o 6017  2_𝑜c2o 6018

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-v 2603  df-dif 2975  df-un 2977  df-nul 3252  df-sn 3404  df-pr 3405  df-suc 4126  df-1o 6024  df-2o 6025

This theorem is referenced by:  2dom  6308