Theorem df2o2 8441

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 8440	. 2 ⊢ 2o = {∅, 1o}
2		df1o2 8439	. . 3 ⊢ 1o = {∅}
3	2	preq2i 4695	. 2 ⊢ {∅, 1o} = {∅, {∅}}
4	1, 3	eqtri 2784	1 ⊢ 2o = {∅, {∅}}

Syntax hints:   = wceq 1559  ∅c0 4285  {csn 4581  {cpr 4583  1_oc1o 8425  2_oc2o 8426

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-tru 1562  df-fal 1572  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-v 3455  df-dif 3907  df-un 3909  df-nul 4286  df-sn 4582  df-pr 4584  df-suc 6348  df-1o 8432  df-2o 8433

This theorem is referenced by:  2dom  9007  pw2eng  9051  pwdju1  10144  canthp1lem1  10607  pr0hash2ex  14418  hashpw  14446  cat1  18113  znidomb  21593  r12  35355  ssoninhaus  36772  onint1  36773  pw2f1ocnv  43578  2omomeqom  43844  df3o3  43855  setc2othin  50051