Theorem df2o2 8531

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 8530	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8529	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4762	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2768	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1537  ∅c0 4352  {csn 4648  {cpr 4650  1_oc1o 8515  2_oc2o 8516

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-v 3490  df-dif 3979  df-un 3981  df-nul 4353  df-sn 4649  df-pr 4651  df-suc 6401  df-1o 8522  df-2o 8523

This theorem is referenced by:  2dom  9095  pw2eng  9144  pwdju1  10260  canthp1lem1  10721  pr0hash2ex  14457  hashpw  14485  cat1  18164  znidomb  21603  ssoninhaus  36414  onint1  36415  pw2f1ocnv  42994  2omomeqom  43265  df3o3  43276  setc2othin  48723