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Theorem df2o2 8107
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 8106 . 2 2o = {∅, 1o}
2 df1o2 8105 . . 3 1o = {∅}
32preq2i 4665 . 2 {∅, 1o} = {∅, {∅}}
41, 3eqtri 2841 1 2o = {∅, {∅}}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1528  c0 4288  {csn 4557  {cpr 4559  1oc1o 8084  2oc2o 8085
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-v 3494  df-dif 3936  df-un 3938  df-nul 4289  df-sn 4558  df-pr 4560  df-suc 6190  df-1o 8091  df-2o 8092
This theorem is referenced by:  2dom  8570  pw2eng  8611  pwdju1  9604  canthp1lem1  10062  pr0hash2ex  13757  hashpw  13785  znidomb  20636  ssoninhaus  33693  onint1  33694  pw2f1ocnv  39512  df3o3  40253
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