Theorem df2o2 8485

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 8484	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8483	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4697	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2783	1 ⊢ 2o = {∅, {∅}}

This proof depends on syntax axioms:   = wceq 1569  ∅c0 4278  {csn 4583  {cpr 4585  1_oc1o 8469  2_oc2o 8470

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-dif 4047  df-un 4151  df-nul 4279  df-sn 4584  df-pr 4586  df-suc 6368  df-1o 8476  df-2o 8477

This theorem is used by:  2dom  9058  pw2eng  9102  pwdju1  10269  canthp1lem1  10737  pr0hash2ex  14552  hashpw  14581  cat1  18272  znidomb  21867  r12  35768  ssoninhaus  37278  onint1  37279  pw2f1ocnv  44086  2omomeqom  44347  df3o3  44358  setc2othin  50616