Theorem df2o2 8472

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 8471	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8470	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4741	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2761	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1542  ∅c0 4322  {csn 4628  {cpr 4630  1_oc1o 8456  2_oc2o 8457

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-dif 3951  df-un 3953  df-nul 4323  df-sn 4629  df-pr 4631  df-suc 6368  df-1o 8463  df-2o 8464

This theorem is referenced by:  2dom  9027  pw2eng  9075  pwdju1  10182  canthp1lem1  10644  pr0hash2ex  14365  hashpw  14393  cat1  18044  znidomb  21109  ssoninhaus  35322  onint1  35323  pw2f1ocnv  41762  2omomeqom  42039  df3o3  42050  setc2othin  47630