Theorem df2o2 8463

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 8462	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8461	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4704	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2786	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1570  ∅c0 4287  {csn 4590  {cpr 4592  1_oc1o 8447  2_oc2o 8448

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1573  df-fal 1583  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-v 3457  df-dif 3909  df-un 3911  df-nul 4288  df-sn 4591  df-pr 4593  df-suc 6368  df-1o 8454  df-2o 8455

This theorem is referenced by:  2dom  9028  pw2eng  9072  pwdju1  10175  canthp1lem1  10638  pr0hash2ex  14446  hashpw  14475  cat1  18155  znidomb  21692  r12  35466  ssoninhaus  36937  onint1  36938  pw2f1ocnv  43744  2omomeqom  44010  df3o3  44021  setc2othin  50221