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Theorem df2o3 6257
Description: Expanded value of the ordinal number 2. (Contributed by Mario Carneiro, 14-Aug-2015.)
Assertion
Ref Expression
df2o3  |-  2o  =  { (/) ,  1o }

Proof of Theorem df2o3
StepHypRef Expression
1 df-2o 6244 . 2  |-  2o  =  suc  1o
2 df-suc 4231 . 2  |-  suc  1o  =  ( 1o  u.  { 1o } )
3 df1o2 6256 . . . 4  |-  1o  =  { (/) }
43uneq1i 3173 . . 3  |-  ( 1o  u.  { 1o }
)  =  ( {
(/) }  u.  { 1o } )
5 df-pr 3481 . . 3  |-  { (/) ,  1o }  =  ( { (/) }  u.  { 1o } )
64, 5eqtr4i 2123 . 2  |-  ( 1o  u.  { 1o }
)  =  { (/) ,  1o }
71, 2, 63eqtri 2124 1  |-  2o  =  { (/) ,  1o }
Colors of variables: wff set class
Syntax hints:    = wceq 1299    u. cun 3019   (/)c0 3310   {csn 3474   {cpr 3475   suc csuc 4225   1oc1o 6236   2oc2o 6237
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 584  ax-in2 585  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082
This theorem depends on definitions:  df-bi 116  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-v 2643  df-dif 3023  df-un 3025  df-nul 3311  df-pr 3481  df-suc 4231  df-1o 6243  df-2o 6244
This theorem is referenced by:  df2o2  6258  2oconcl  6266  0lt2o  6268  1lt2o  6269  en2eqpr  6730  finomni  6924  exmidomniim  6925  exmidomni  6926  exmidfodomrlemr  6967  exmidfodomrlemrALT  6968  xp2dju  6975  el2oss1o  12773  nninfalllem1  12787  nninfall  12788  nninfsellemqall  12795  nninfomnilem  12798  isomninnlem  12809
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