Theorem df2o2 8471

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 8470	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8469	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4740	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2760	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1541  ∅c0 4321  {csn 4627  {cpr 4629  1_oc1o 8455  2_oc2o 8456

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476  df-dif 3950  df-un 3952  df-nul 4322  df-sn 4628  df-pr 4630  df-suc 6367  df-1o 8462  df-2o 8463

This theorem is referenced by:  2dom  9026  pw2eng  9074  pwdju1  10181  canthp1lem1  10643  pr0hash2ex  14364  hashpw  14392  cat1  18043  znidomb  21108  ssoninhaus  35321  onint1  35322  pw2f1ocnv  41761  2omomeqom  42038  df3o3  42049  setc2othin  47629