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Theorem df2o2 7461
 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 7460 . 2 2𝑜 = {∅, 1𝑜}
2 df1o2 7459 . . 3 1𝑜 = {∅}
32preq2i 4216 . 2 {∅, 1𝑜} = {∅, {∅}}
41, 3eqtri 2632 1 2𝑜 = {∅, {∅}}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475  ∅c0 3874  {csn 4125  {cpr 4127  1𝑜c1o 7440  2𝑜c2o 7441 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-dif 3543  df-un 3545  df-nul 3875  df-sn 4126  df-pr 4128  df-suc 5646  df-1o 7447  df-2o 7448 This theorem is referenced by:  2dom  7915  pw2eng  7951  pwcda1  8899  canthp1lem1  9353  pr0hash2ex  13057  hashpw  13083  znidomb  19729  ssoninhaus  31617  onint1  31618  pw2f1ocnv  36622  df3o3  37343
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