Theorem df2o2 8306

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 8305	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8304	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4673	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2766	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1539  ∅c0 4256  {csn 4561  {cpr 4563  1_oc1o 8290  2_oc2o 8291

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1542  df-fal 1552  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-dif 3890  df-un 3892  df-nul 4257  df-sn 4562  df-pr 4564  df-suc 6272  df-1o 8297  df-2o 8298

This theorem is referenced by:  2dom  8820  pw2eng  8865  pwdju1  9946  canthp1lem1  10408  pr0hash2ex  14123  hashpw  14151  cat1  17812  znidomb  20769  ssoninhaus  34637  onint1  34638  pw2f1ocnv  40859  df3o3  41635  setc2othin  46337