Theorem df2o2 8218

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 8217	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8214	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4653	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2765	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1543  ∅c0 4237  {csn 4541  {cpr 4543  1_oc1o 8195  2_oc2o 8196

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-ext 2708

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-tru 1546  df-fal 1556  df-ex 1788  df-sb 2071  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3410  df-dif 3869  df-un 3871  df-nul 4238  df-sn 4542  df-pr 4544  df-suc 6219  df-1o 8202  df-2o 8203

This theorem is referenced by:  2dom  8707  pw2eng  8751  pwdju1  9804  canthp1lem1  10266  pr0hash2ex  13975  hashpw  14003  cat1  17603  znidomb  20526  ssoninhaus  34374  onint1  34375  pw2f1ocnv  40562  df3o3  41312  setc2othin  46010