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Theorem df2o2 6280
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 6279 . 2  |-  2o  =  { (/) ,  1o }
2 df1o2 6278 . . 3  |-  1o  =  { (/) }
32preq2i 3568 . 2  |-  { (/) ,  1o }  =  { (/)
,  { (/) } }
41, 3eqtri 2133 1  |-  2o  =  { (/) ,  { (/) } }
Colors of variables: wff set class
Syntax hints:    = wceq 1312   (/)c0 3327   {csn 3491   {cpr 3492   1oc1o 6258   2oc2o 6259
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681  ax-5 1404  ax-7 1405  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-10 1464  ax-11 1465  ax-i12 1466  ax-bndl 1467  ax-4 1468  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-i5r 1496  ax-ext 2095
This theorem depends on definitions:  df-bi 116  df-tru 1315  df-nf 1418  df-sb 1717  df-clab 2100  df-cleq 2106  df-clel 2109  df-nfc 2242  df-v 2657  df-dif 3037  df-un 3039  df-nul 3328  df-sn 3497  df-pr 3498  df-suc 4251  df-1o 6265  df-2o 6266
This theorem is referenced by:  2dom  6651  exmidpw  6753  pr0hash2ex  10448  ss1oel2o  12872
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