Theorem df2o2 8516

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 8515	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8514	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4736	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2764	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1539  ∅c0 4332  {csn 4625  {cpr 4627  1_oc1o 8500  2_oc2o 8501

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-dif 3953  df-un 3955  df-nul 4333  df-sn 4626  df-pr 4628  df-suc 6389  df-1o 8507  df-2o 8508

This theorem is referenced by:  2dom  9071  pw2eng  9119  pwdju1  10232  canthp1lem1  10693  pr0hash2ex  14448  hashpw  14476  cat1  18143  znidomb  21581  ssoninhaus  36450  onint1  36451  pw2f1ocnv  43054  2omomeqom  43321  df3o3  43332  setc2othin  49138