Theorem df2o2 8283

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 8282	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8279	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4670	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2766	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1539  ∅c0 4253  {csn 4558  {cpr 4560  1_oc1o 8260  2_oc2o 8261

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1542  df-fal 1552  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-dif 3886  df-un 3888  df-nul 4254  df-sn 4559  df-pr 4561  df-suc 6257  df-1o 8267  df-2o 8268

This theorem is referenced by:  2dom  8774  pw2eng  8818  pwdju1  9877  canthp1lem1  10339  pr0hash2ex  14051  hashpw  14079  cat1  17728  znidomb  20681  ssoninhaus  34564  onint1  34565  pw2f1ocnv  40775  df3o3  41524  setc2othin  46225