Theorem df2o2 8475

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 8474	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8473	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4742	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2761	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1542  ∅c0 4323  {csn 4629  {cpr 4631  1_oc1o 8459  2_oc2o 8460

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 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-dif 3952  df-un 3954  df-nul 4324  df-sn 4630  df-pr 4632  df-suc 6371  df-1o 8466  df-2o 8467

This theorem is referenced by:  2dom  9030  pw2eng  9078  pwdju1  10185  canthp1lem1  10647  pr0hash2ex  14368  hashpw  14396  cat1  18047  znidomb  21117  ssoninhaus  35333  onint1  35334  pw2f1ocnv  41776  2omomeqom  42053  df3o3  42064  setc2othin  47676