Theorem df2o2 8514

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 8513	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8512	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4742	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2763	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1537  ∅c0 4339  {csn 4631  {cpr 4633  1_oc1o 8498  2_oc2o 8499

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-dif 3966  df-un 3968  df-nul 4340  df-sn 4632  df-pr 4634  df-suc 6392  df-1o 8505  df-2o 8506

This theorem is referenced by:  2dom  9069  pw2eng  9117  pwdju1  10229  canthp1lem1  10690  pr0hash2ex  14444  hashpw  14472  cat1  18151  znidomb  21598  ssoninhaus  36431  onint1  36432  pw2f1ocnv  43026  2omomeqom  43293  df3o3  43304  setc2othin  48857