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Theorem df2o3 6327
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 6314 . 2  |-  2o  =  suc  1o
2 df-suc 4293 . 2  |-  suc  1o  =  ( 1o  u.  { 1o } )
3 df1o2 6326 . . . 4  |-  1o  =  { (/) }
43uneq1i 3226 . . 3  |-  ( 1o  u.  { 1o }
)  =  ( {
(/) }  u.  { 1o } )
5 df-pr 3534 . . 3  |-  { (/) ,  1o }  =  ( { (/) }  u.  { 1o } )
64, 5eqtr4i 2163 . 2  |-  ( 1o  u.  { 1o }
)  =  { (/) ,  1o }
71, 2, 63eqtri 2164 1  |-  2o  =  { (/) ,  1o }
Colors of variables: wff set class
Syntax hints:    = wceq 1331    u. cun 3069   (/)c0 3363   {csn 3527   {cpr 3528   suc csuc 4287   1oc1o 6306   2oc2o 6307
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-dif 3073  df-un 3075  df-nul 3364  df-pr 3534  df-suc 4293  df-1o 6313  df-2o 6314
This theorem is referenced by:  df2o2  6328  2oconcl  6336  0lt2o  6338  1lt2o  6339  en2eqpr  6801  finomni  7012  exmidomniim  7013  exmidomni  7014  ismkvnex  7029  exmidfodomrlemr  7063  exmidfodomrlemrALT  7064  xp2dju  7076  unct  11966  el2oss1o  13272  nninfalllem1  13289  nninfall  13290  nninfsellemqall  13297  nninfomnilem  13300  isomninnlem  13311
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