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Theorem df2o2 8471
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 8470 . 2 2o = {∅, 1o}
2 df1o2 8469 . . 3 1o = {∅}
32preq2i 4740 . 2 {∅, 1o} = {∅, {∅}}
41, 3eqtri 2760 1 2o = {∅, {∅}}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1541  c0 4321  {csn 4627  {cpr 4629  1oc1o 8455  2oc2o 8456
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476  df-dif 3950  df-un 3952  df-nul 4322  df-sn 4628  df-pr 4630  df-suc 6367  df-1o 8462  df-2o 8463
This theorem is referenced by:  2dom  9026  pw2eng  9074  pwdju1  10181  canthp1lem1  10643  pr0hash2ex  14364  hashpw  14392  cat1  18043  znidomb  21108  ssoninhaus  35321  onint1  35322  pw2f1ocnv  41761  2omomeqom  42038  df3o3  42049  setc2othin  47629
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