Theorem df2o2 8400

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 8399	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8398	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4689	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2756	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1541  ∅c0 4282  {csn 4575  {cpr 4577  1_oc1o 8384  2_oc2o 8385

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 2705

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 2712  df-cleq 2725  df-clel 2808  df-v 3439  df-dif 3901  df-un 3903  df-nul 4283  df-sn 4576  df-pr 4578  df-suc 6317  df-1o 8391  df-2o 8392

This theorem is referenced by:  2dom  8959  pw2eng  9003  pwdju1  10089  canthp1lem1  10550  pr0hash2ex  14317  hashpw  14345  cat1  18006  znidomb  21500  r12  35127  ssoninhaus  36513  onint1  36514  pw2f1ocnv  43154  2omomeqom  43420  df3o3  43431  setc2othin  49591