Theorem df2o2 6589

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 6588	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 6587	. . 3 ⊢ 1o = {∅}
3	2	preq2i 3747	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2250	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1395  ∅c0 3491  {csn 3666  {cpr 3667  1_oc1o 6566  2_oc2o 6567

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-dif 3199  df-un 3201  df-nul 3492  df-sn 3672  df-pr 3673  df-suc 4463  df-1o 6573  df-2o 6574

This theorem is referenced by:  2dom  6971  exmidpw  7086  exmidpweq  7087  exmidpw2en  7090  pr0hash2ex  11055  ss1oel2o  16464