Theorem df2o2 8494

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 8493	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8492	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4718	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2759	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1540  ∅c0 4313  {csn 4606  {cpr 4608  1_oc1o 8478  2_oc2o 8479

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2715  df-cleq 2728  df-clel 2810  df-v 3466  df-dif 3934  df-un 3936  df-nul 4314  df-sn 4607  df-pr 4609  df-suc 6363  df-1o 8485  df-2o 8486

This theorem is referenced by:  2dom  9049  pw2eng  9097  pwdju1  10210  canthp1lem1  10671  pr0hash2ex  14431  hashpw  14459  cat1  18115  znidomb  21527  ssoninhaus  36471  onint1  36472  pw2f1ocnv  43028  2omomeqom  43294  df3o3  43305  setc2othin  49319