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Theorem df2o2 8119
 Description: Expanded value of the ordinal number 2. (Contributed by NM, 29-Jan-2004.)
Assertion
Ref Expression
df2o2 2o = {∅, {∅}}

Proof of Theorem df2o2
StepHypRef Expression
1 df2o3 8118 . 2 2o = {∅, 1o}
2 df1o2 8117 . . 3 1o = {∅}
32preq2i 4636 . 2 {∅, 1o} = {∅, {∅}}
41, 3eqtri 2821 1 2o = {∅, {∅}}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538  ∅c0 4246  {csn 4528  {cpr 4530  1oc1o 8096  2oc2o 8097 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 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3444  df-dif 3886  df-un 3888  df-nul 4247  df-sn 4529  df-pr 4531  df-suc 6172  df-1o 8103  df-2o 8104 This theorem is referenced by:  2dom  8583  pw2eng  8624  pwdju1  9619  canthp1lem1  10081  pr0hash2ex  13785  hashpw  13813  znidomb  20275  ssoninhaus  34056  onint1  34057  pw2f1ocnv  40149  df3o3  40899
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