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Theorem df2o2 6676
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 6675 . 2  |-  2o  =  { (/) ,  1o }
2 df1o2 6674 . . 3  |-  1o  =  { (/) }
32preq2i 3832 . 2  |-  { (/) ,  1o }  =  { (/)
,  { (/) } }
41, 3eqtri 2409 1  |-  2o  =  { (/) ,  { (/) } }
Colors of variables: wff set class
Syntax hints:    = wceq 1649   (/)c0 3573   {csn 3759   {cpr 3760   1oc1o 6655   2oc2o 6656
This theorem is referenced by:  2dom  7117  pw2eng  7152  pwcda1  8009  canthp1lem1  8462  hashpw  11628  znidomb  16767  ssoninhaus  25914  onint1  25915  pw2f1ocnv  26801
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-v 2903  df-dif 3268  df-un 3270  df-nul 3574  df-sn 3765  df-pr 3766  df-suc 4530  df-1o 6662  df-2o 6663
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