Theorem df2o2 8407

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 8406	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8405	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4682	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2760	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1542  ∅c0 4274  {csn 4568  {cpr 4570  1_oc1o 8391  2_oc2o 8392

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 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3432  df-dif 3893  df-un 3895  df-nul 4275  df-sn 4569  df-pr 4571  df-suc 6323  df-1o 8398  df-2o 8399

This theorem is referenced by:  2dom  8970  pw2eng  9014  pwdju1  10104  canthp1lem1  10566  pr0hash2ex  14361  hashpw  14389  cat1  18055  znidomb  21551  r12  35254  ssoninhaus  36646  onint1  36647  pw2f1ocnv  43483  2omomeqom  43749  df3o3  43760  setc2othin  49953