Theorem df2o2 8446

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 8445	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8444	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4704	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2753	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1540  ∅c0 4299  {csn 4592  {cpr 4594  1_oc1o 8430  2_oc2o 8431

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-v 3452  df-dif 3920  df-un 3922  df-nul 4300  df-sn 4593  df-pr 4595  df-suc 6341  df-1o 8437  df-2o 8438

This theorem is referenced by:  2dom  9004  pw2eng  9052  pwdju1  10151  canthp1lem1  10612  pr0hash2ex  14380  hashpw  14408  cat1  18066  znidomb  21478  ssoninhaus  36443  onint1  36444  pw2f1ocnv  43033  2omomeqom  43299  df3o3  43310  setc2othin  49459