Theorem df2o2 7574

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 7573	. 2 |- 2o = { (/) , 1o }
2		df1o2 7572	. . 3 |- 1o = { (/) }
3	2	preq2i 4272	. 2 |- { (/) , 1o } = { (/) , { (/) } }
4	1, 3	eqtri 2644	1 |- 2o = { (/) , { (/) } }

Syntax hints:   = wceq 1483   (/)c0 3915   {csn 4177   {cpr 4179   1oc1o 7553   2oc2o 7554

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-dif 3577  df-un 3579  df-nul 3916  df-sn 4178  df-pr 4180  df-suc 5729  df-1o 7560  df-2o 7561

This theorem is referenced by:  2dom  8029  pw2eng  8066  pwcda1  9016  canthp1lem1  9474  pr0hash2ex  13196  hashpw  13223  znidomb  19910  ssoninhaus  32447  onint1  32448  pw2f1ocnv  37604  df3o3  38323