Theorem df2o2 8489

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 8488	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8487	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4737	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2755	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1534  ∅c0 4318  {csn 4624  {cpr 4626  1_oc1o 8473  2_oc2o 8474

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2698

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2705  df-cleq 2719  df-clel 2805  df-v 3471  df-dif 3947  df-un 3949  df-nul 4319  df-sn 4625  df-pr 4627  df-suc 6369  df-1o 8480  df-2o 8481

This theorem is referenced by:  2dom  9046  pw2eng  9094  pwdju1  10205  canthp1lem1  10667  pr0hash2ex  14391  hashpw  14419  cat1  18077  znidomb  21482  ssoninhaus  35868  onint1  35869  pw2f1ocnv  42380  2omomeqom  42655  df3o3  42666  setc2othin  47985