Theorem df2o2 7461

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 7460	. 2 ⊢ 2𝑜 = {∅, 1𝑜}
2		df1o2 7459	. . 3 ⊢ 1𝑜 = {∅}
3	2	preq2i 4216	. 2 ⊢ {∅, 1𝑜} = {∅, {∅}}
4	1, 3	eqtri 2632	1 ⊢ 2𝑜 = {∅, {∅}}

Syntax hints:   = wceq 1475  ∅c0 3874  {csn 4125  {cpr 4127  1_𝑜c1o 7440  2_𝑜c2o 7441

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-dif 3543  df-un 3545  df-nul 3875  df-sn 4126  df-pr 4128  df-suc 5646  df-1o 7447  df-2o 7448

This theorem is referenced by:  2dom  7915  pw2eng  7951  pwcda1  8899  canthp1lem1  9353  pr0hash2ex  13057  hashpw  13083  znidomb  19729  ssoninhaus  31617  onint1  31618  pw2f1ocnv  36622  df3o3  37343