Theorem df2o2 8450

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 8449	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8448	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4699	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2788	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1563  ∅c0 4288  {csn 4585  {cpr 4587  1_oc1o 8434  2_oc2o 8435

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-8 2147  ax-9 2155  ax-ext 2737

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1566  df-fal 1576  df-ex 1803  df-sb 2094  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-dif 3910  df-un 3912  df-nul 4289  df-sn 4586  df-pr 4588  df-suc 6356  df-1o 8441  df-2o 8442

This theorem is referenced by:  2dom  9015  pw2eng  9059  pwdju1  10162  canthp1lem1  10625  pr0hash2ex  14435  hashpw  14463  cat1  18144  znidomb  21671  r12  35403  ssoninhaus  36821  onint1  36822  pw2f1ocnv  43626  2omomeqom  43892  df3o3  43903  setc2othin  50095