Theorem df2o2 8469

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 8468	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8467	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4698	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2784	1 ⊢ 2o = {∅, {∅}}

This proof depends on syntax axioms:   = wceq 1570  ∅c0 4279  {csn 4584  {cpr 4586  1_oc1o 8453  2_oc2o 8454

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2733

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2740  df-cleq 2753  df-clel 2836  df-v 3453  df-dif 3902  df-un 3904  df-nul 4280  df-sn 4585  df-pr 4587  df-suc 6361  df-1o 8460  df-2o 8461

This theorem is used by:  2dom  9042  pw2eng  9086  pwdju1  10250  canthp1lem1  10718  pr0hash2ex  14532  hashpw  14561  cat1  18252  znidomb  21847  r12  35705  ssoninhaus  37206  onint1  37207  pw2f1ocnv  43997  2omomeqom  44263  df3o3  44274  setc2othin  50518