Theorem df2o2 8443

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 8442	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8441	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4701	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2752	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1540  ∅c0 4296  {csn 4589  {cpr 4591  1_oc1o 8427  2_oc2o 8428

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 2701

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 2708  df-cleq 2721  df-clel 2803  df-v 3449  df-dif 3917  df-un 3919  df-nul 4297  df-sn 4590  df-pr 4592  df-suc 6338  df-1o 8434  df-2o 8435

This theorem is referenced by:  2dom  9001  pw2eng  9047  pwdju1  10144  canthp1lem1  10605  pr0hash2ex  14373  hashpw  14401  cat1  18059  znidomb  21471  ssoninhaus  36436  onint1  36437  pw2f1ocnv  43026  2omomeqom  43292  df3o3  43303  setc2othin  49455