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Theorem df2o3 6448
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 6435 . 2  |-  2o  =  suc  1o
2 df-suc 4385 . 2  |-  suc  1o  =  ( 1o  u.  { 1o } )
3 df1o2 6447 . . . 4  |-  1o  =  { (/) }
43uneq1i 3299 . . 3  |-  ( 1o  u.  { 1o }
)  =  ( {
(/) }  u.  { 1o } )
5 df-pr 3613 . . 3  |-  { (/) ,  1o }  =  ( { (/) }  u.  { 1o } )
64, 5eqtr4i 2212 . 2  |-  ( 1o  u.  { 1o }
)  =  { (/) ,  1o }
71, 2, 63eqtri 2213 1  |-  2o  =  { (/) ,  1o }
Colors of variables: wff set class
Syntax hints:    = wceq 1363    u. cun 3141   (/)c0 3436   {csn 3606   {cpr 3607   suc csuc 4379   1oc1o 6427   2oc2o 6428
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2170
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2175  df-cleq 2181  df-clel 2184  df-nfc 2320  df-v 2753  df-dif 3145  df-un 3147  df-nul 3437  df-pr 3613  df-suc 4385  df-1o 6434  df-2o 6435
This theorem is referenced by:  df2o2  6449  2oconcl  6457  0lt2o  6459  1lt2o  6460  el2oss1o  6461  en2eqpr  6924  nninfisol  7148  finomni  7155  exmidomniim  7156  exmidomni  7157  ismkvnex  7170  nninfwlpoimlemginf  7191  exmidfodomrlemr  7218  exmidfodomrlemrALT  7219  xp2dju  7231  pw1nel3  7247  sucpw1nel3  7249  unct  12460  fnpr2o  12780  fnpr2ob  12781  fvprif  12784  xpsfrnel  12785  xpsfeq  12786  2o01f  15130  nninfalllem1  15141  nninfall  15142  nninfsellemqall  15148  nninfomnilem  15151
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