Theorem df2o2 6665

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 6664	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 6663	. . 3 ⊢ 1o = {∅}
3	2	preq2i 3774	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2255	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1398  ∅c0 3510  {csn 3691  {cpr 3692  1_oc1o 6642  2_oc2o 6643

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-v 2817  df-dif 3215  df-un 3217  df-nul 3511  df-sn 3697  df-pr 3698  df-suc 4494  df-1o 6649  df-2o 6650

This theorem is referenced by:  2dom  7048  exmidpw  7170  exmidpweq  7171  exmidpw2en  7174  pr0hash2ex  11188  ss1oel2o  16810