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Theorem df2o2 6152
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 6151 . 2  |-  2o  =  { (/) ,  1o }
2 df1o2 6150 . . 3  |-  1o  =  { (/) }
32preq2i 3508 . 2  |-  { (/) ,  1o }  =  { (/)
,  { (/) } }
41, 3eqtri 2105 1  |-  2o  =  { (/) ,  { (/) } }
Colors of variables: wff set class
Syntax hints:    = wceq 1287   (/)c0 3275   {csn 3431   {cpr 3432   1oc1o 6130   2oc2o 6131
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2617  df-dif 2990  df-un 2992  df-nul 3276  df-sn 3437  df-pr 3438  df-suc 4174  df-1o 6137  df-2o 6138
This theorem is referenced by:  2dom  6476  exmidpw  6578  pr0hash2ex  10123  ss1oel2o  11357
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