Theorem df2o2 8411

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 8410	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8409	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4676	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2763	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1547  ∅c0 4268  {csn 4562  {cpr 4564  1_oc1o 8395  2_oc2o 8396

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-tru 1550  df-fal 1560  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-v 3434  df-dif 3893  df-un 3895  df-nul 4269  df-sn 4563  df-pr 4565  df-suc 6323  df-1o 8402  df-2o 8403

This theorem is referenced by:  2dom  8974  pw2eng  9018  pwdju1  10111  canthp1lem1  10573  pr0hash2ex  14368  hashpw  14396  cat1  18062  znidomb  21543  r12  35283  ssoninhaus  36683  onint1  36684  pw2f1ocnv  43489  2omomeqom  43755  df3o3  43766  setc2othin  49963