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Theorem df2o3 7460
 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 7448 . 2 2𝑜 = suc 1𝑜
2 df-suc 5646 . 2 suc 1𝑜 = (1𝑜 ∪ {1𝑜})
3 df1o2 7459 . . . 4 1𝑜 = {∅}
43uneq1i 3725 . . 3 (1𝑜 ∪ {1𝑜}) = ({∅} ∪ {1𝑜})
5 df-pr 4128 . . 3 {∅, 1𝑜} = ({∅} ∪ {1𝑜})
64, 5eqtr4i 2635 . 2 (1𝑜 ∪ {1𝑜}) = {∅, 1𝑜}
71, 2, 63eqtri 2636 1 2𝑜 = {∅, 1𝑜}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475   ∪ cun 3538  ∅c0 3874  {csn 4125  {cpr 4127  suc csuc 5642  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-pr 4128  df-suc 5646  df-1o 7447  df-2o 7448 This theorem is referenced by:  df2o2  7461  2oconcl  7470  map2xp  8015  1sdom  8048  cantnflem2  8470  xp2cda  8885  sdom2en01  9007  sadcf  15013  xpscfn  16042  xpscfv  16045  xpsfrnel  16046  xpsfeq  16047  xpsfrnel2  16048  xpsle  16064  setcepi  16561  efgi0  17956  efgi1  17957  vrgpf  18004  vrgpinv  18005  frgpuptinv  18007  frgpup2  18012  frgpup3lem  18013  frgpnabllem1  18099  dmdprdpr  18271  dprdpr  18272  xpstopnlem1  21422  xpstopnlem2  21424  xpsxmetlem  21994  xpsdsval  21996  xpsmet  21997  onint1  31618  pw2f1ocnv  36622  wepwsolem  36630  df3o2  37342  clsk1independent  37364
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