Theorem df2o2 6603

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 6602	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 6601	. . 3 ⊢ 1o = {∅}
3	2	preq2i 3753	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2251	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1397  ∅c0 3493  {csn 3670  {cpr 3671  1_oc1o 6580  2_oc2o 6581

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 619  ax-in2 620  ax-io 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2212

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1810  df-clab 2217  df-cleq 2223  df-clel 2226  df-nfc 2362  df-v 2803  df-dif 3201  df-un 3203  df-nul 3494  df-sn 3676  df-pr 3677  df-suc 4470  df-1o 6587  df-2o 6588

This theorem is referenced by:  2dom  6985  exmidpw  7105  exmidpweq  7106  exmidpw2en  7109  pr0hash2ex  11085  ss1oel2o  16646