Theorem df2o2 8406

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 8405	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8404	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4694	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2759	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1541  ∅c0 4285  {csn 4580  {cpr 4582  1_oc1o 8390  2_oc2o 8391

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3442  df-dif 3904  df-un 3906  df-nul 4286  df-sn 4581  df-pr 4583  df-suc 6323  df-1o 8397  df-2o 8398

This theorem is referenced by:  2dom  8967  pw2eng  9011  pwdju1  10101  canthp1lem1  10563  pr0hash2ex  14331  hashpw  14359  cat1  18021  znidomb  21516  r12  35251  ssoninhaus  36642  onint1  36643  pw2f1ocnv  43275  2omomeqom  43541  df3o3  43552  setc2othin  49707