Theorem df2o2 8394

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 8393	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8392	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4690	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2754	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1541  ∅c0 4283  {csn 4576  {cpr 4578  1_oc1o 8378  2_oc2o 8379

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-v 3438  df-dif 3905  df-un 3907  df-nul 4284  df-sn 4577  df-pr 4579  df-suc 6312  df-1o 8385  df-2o 8386

This theorem is referenced by:  2dom  8952  pw2eng  8996  pwdju1  10079  canthp1lem1  10540  pr0hash2ex  14312  hashpw  14340  cat1  18001  znidomb  21496  ssoninhaus  36481  onint1  36482  pw2f1ocnv  43069  2omomeqom  43335  df3o3  43346  setc2othin  49497