Theorem df2o2 6547

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 6546	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 6545	. . 3 ⊢ 1o = {∅}
3	2	preq2i 3727	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2230	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1375  ∅c0 3471  {csn 3646  {cpr 3647  1_oc1o 6525  2_oc2o 6526

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 617  ax-in2 618  ax-io 713  ax-5 1473  ax-7 1474  ax-gen 1475  ax-ie1 1519  ax-ie2 1520  ax-8 1530  ax-10 1531  ax-11 1532  ax-i12 1533  ax-bndl 1535  ax-4 1536  ax-17 1552  ax-i9 1556  ax-ial 1560  ax-i5r 1561  ax-ext 2191

This theorem depends on definitions:  df-bi 117  df-tru 1378  df-nf 1487  df-sb 1789  df-clab 2196  df-cleq 2202  df-clel 2205  df-nfc 2341  df-v 2781  df-dif 3179  df-un 3181  df-nul 3472  df-sn 3652  df-pr 3653  df-suc 4439  df-1o 6532  df-2o 6533

This theorem is referenced by:  2dom  6928  exmidpw  7038  exmidpweq  7039  exmidpw2en  7042  pr0hash2ex  11004  ss1oel2o  16265