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Theorem df2o3 6430
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 6417 . 2 2o = suc 1o
2 df-suc 4371 . 2 suc 1o = (1o ∪ {1o})
3 df1o2 6429 . . . 4 1o = {∅}
43uneq1i 3285 . . 3 (1o ∪ {1o}) = ({∅} ∪ {1o})
5 df-pr 3599 . . 3 {∅, 1o} = ({∅} ∪ {1o})
64, 5eqtr4i 2201 . 2 (1o ∪ {1o}) = {∅, 1o}
71, 2, 63eqtri 2202 1 2o = {∅, 1o}
Colors of variables: wff set class
Syntax hints:   = wceq 1353  cun 3127  c0 3422  {csn 3592  {cpr 3593  suc csuc 4365  1oc1o 6409  2oc2o 6410
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 614  ax-in2 615  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-dif 3131  df-un 3133  df-nul 3423  df-pr 3599  df-suc 4371  df-1o 6416  df-2o 6417
This theorem is referenced by:  df2o2  6431  2oconcl  6439  0lt2o  6441  1lt2o  6442  el2oss1o  6443  en2eqpr  6906  nninfisol  7130  finomni  7137  exmidomniim  7138  exmidomni  7139  ismkvnex  7152  nninfwlpoimlemginf  7173  exmidfodomrlemr  7200  exmidfodomrlemrALT  7201  xp2dju  7213  pw1nel3  7229  sucpw1nel3  7231  unct  12442  fnpr2o  12757  fnpr2ob  12758  fvprif  12761  xpsfrnel  12762  xpsfeq  12763  2o01f  14716  nninfalllem1  14727  nninfall  14728  nninfsellemqall  14734  nninfomnilem  14737
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