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Theorem df2o2 6335
 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 6334 . 2 2o = {∅, 1o}
2 df1o2 6333 . . 3 1o = {∅}
32preq2i 3611 . 2 {∅, 1o} = {∅, {∅}}
41, 3eqtri 2161 1 2o = {∅, {∅}}
 Colors of variables: wff set class Syntax hints:   = wceq 1332  ∅c0 3367  {csn 3531  {cpr 3532  1oc1o 6313  2oc2o 6314 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 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-dif 3077  df-un 3079  df-nul 3368  df-sn 3537  df-pr 3538  df-suc 4300  df-1o 6320  df-2o 6321 This theorem is referenced by:  2dom  6706  exmidpw  6809  pr0hash2ex  10592  ss1oel2o  13358
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