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 4742	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2753	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1533  ∅c0 4323  {csn 4629  {cpr 4631  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 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-v 3465  df-dif 3948  df-un 3950  df-nul 4324  df-sn 4630  df-pr 4632  df-suc 6375  df-1o 8485  df-2o 8486

This theorem is referenced by:  2dom  9053  pw2eng  9101  pwdju1  10213  canthp1lem1  10675  pr0hash2ex  14399  hashpw  14427  cat1  18085  znidomb  21499  ssoninhaus  36002  onint1  36003  pw2f1ocnv  42523  2omomeqom  42797  df3o3  42808  setc2othin  48174