Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  df2o2 Structured version   Unicode version

Theorem df2o2 6730
 Description: Expanded value of the ordinal number 2. (Contributed by NM, 29-Jan-2004.)
Assertion
Ref Expression
df2o2

Proof of Theorem df2o2
StepHypRef Expression
1 df2o3 6729 . 2
2 df1o2 6728 . . 3
32preq2i 3879 . 2
41, 3eqtri 2455 1
 Colors of variables: wff set class Syntax hints:   wceq 1652  c0 3620  csn 3806  cpr 3807  c1o 6709  c2o 6710 This theorem is referenced by:  2dom  7171  pw2eng  7206  pwcda1  8066  canthp1lem1  8519  hashpw  11691  znidomb  16834  ssoninhaus  26190  onint1  26191  pw2f1ocnv  27099 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-dif 3315  df-un 3317  df-nul 3621  df-sn 3812  df-pr 3813  df-suc 4579  df-1o 6716  df-2o 6717
 Copyright terms: Public domain W3C validator