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Theorem df2o2 7136
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 7135 . 2  |-  2o  =  { (/) ,  1o }
2 df1o2 7134 . . 3  |-  1o  =  { (/) }
32preq2i 4099 . 2  |-  { (/) ,  1o }  =  { (/)
,  { (/) } }
41, 3eqtri 2483 1  |-  2o  =  { (/) ,  { (/) } }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1398   (/)c0 3783   {csn 4016   {cpr 4018   1oc1o 7115   2oc2o 7116
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-v 3108  df-dif 3464  df-un 3466  df-nul 3784  df-sn 4017  df-pr 4019  df-suc 4873  df-1o 7122  df-2o 7123
This theorem is referenced by:  2dom  7581  pw2eng  7616  pwcda1  8565  canthp1lem1  9019  pr0hash2ex  12457  hashpw  12478  znidomb  18773  ssoninhaus  30141  onint1  30142  pw2f1ocnv  31218
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