Theorem df2o2 6697

Description: Expanded value of the ordinal number 2. (Contributed by NM, 29-Jan-2004.)

Assertion

Ref	Expression
df2o2	⊢ 2o = {∅, {∅}}

Proof of Theorem df2o2

Step	Hyp	Ref	Expression
1		df2o3 6696	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 6695	. . 3 ⊢ 1o = {∅}
3	2	preq2i 3791	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2259	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1402  ∅c0 3520  {csn 3708  {cpr 3709  1_oc1o 6674  2_oc2o 6675

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 623  ax-in2 624  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-v 2823  df-dif 3222  df-un 3224  df-nul 3521  df-sn 3714  df-pr 3715  df-suc 4514  df-1o 6681  df-2o 6682

This theorem is referenced by:  2dom  7087  exmidpw  7209  exmidpweq  7210  exmidpw2en  7213  pr0hash2ex  11239  ss1oel2o  17000