ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df1o2 GIF version

Theorem df1o2 6043
Description: Expanded value of the ordinal number 1. (Contributed by NM, 4-Nov-2002.)
Assertion
Ref Expression
df1o2 1𝑜 = {∅}

Proof of Theorem df1o2
StepHypRef Expression
1 df-1o 6031 . 2 1𝑜 = suc ∅
2 suc0 4175 . 2 suc ∅ = {∅}
31, 2eqtri 2076 1 1𝑜 = {∅}
Colors of variables: wff set class
Syntax hints:   = wceq 1259  c0 3251  {csn 3402  suc csuc 4129  1𝑜c1o 6024
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-dif 2947  df-un 2949  df-nul 3252  df-suc 4135  df-1o 6031
This theorem is referenced by:  df2o3  6044  df2o2  6045  1n0  6046  el1o  6050  dif1o  6051  ensn1  6306  en1  6309  xp1en  6327
  Copyright terms: Public domain W3C validator