Theorem df2o2 8110

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 8109	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8108	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4665	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2842	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1531  ∅c0 4289  {csn 4559  {cpr 4561  1_oc1o 8087  2_oc2o 8088

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1905  ax-6 1964  ax-7 2009  ax-8 2110  ax-9 2118  ax-10 2139  ax-11 2154  ax-12 2170  ax-ext 2791

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1534  df-ex 1775  df-nf 1779  df-sb 2064  df-clab 2798  df-cleq 2812  df-clel 2891  df-nfc 2961  df-v 3495  df-dif 3937  df-un 3939  df-nul 4290  df-sn 4560  df-pr 4562  df-suc 6190  df-1o 8094  df-2o 8095

This theorem is referenced by:  2dom  8574  pw2eng  8615  pwdju1  9608  canthp1lem1  10066  pr0hash2ex  13761  hashpw  13789  znidomb  20700  ssoninhaus  33789  onint1  33790  pw2f1ocnv  39624  df3o3  40365