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Theorem df2o3 6330
 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 6317 . 2 2o = suc 1o
2 df-suc 4296 . 2 suc 1o = (1o ∪ {1o})
3 df1o2 6329 . . . 4 1o = {∅}
43uneq1i 3226 . . 3 (1o ∪ {1o}) = ({∅} ∪ {1o})
5 df-pr 3534 . . 3 {∅, 1o} = ({∅} ∪ {1o})
64, 5eqtr4i 2163 . 2 (1o ∪ {1o}) = {∅, 1o}
71, 2, 63eqtri 2164 1 2o = {∅, 1o}
 Colors of variables: wff set class Syntax hints:   = wceq 1331   ∪ cun 3069  ∅c0 3363  {csn 3527  {cpr 3528  suc csuc 4290  1oc1o 6309  2oc2o 6310 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 4296  df-1o 6316  df-2o 6317 This theorem is referenced by:  df2o2  6331  2oconcl  6339  0lt2o  6341  1lt2o  6342  en2eqpr  6804  finomni  7015  exmidomniim  7016  exmidomni  7017  ismkvnex  7032  exmidfodomrlemr  7070  exmidfodomrlemrALT  7071  xp2dju  7083  unct  11978  el2oss1o  13332  2o01f  13337  nninfalllem1  13351  nninfall  13352  nninfsellemqall  13359  nninfomnilem  13362
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