Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  df3o2 Structured version   Visualization version   GIF version

Theorem df3o2 40254
Description: Ordinal 3 is the triplet containing ordinals 0, 1 and 2. (Contributed by RP, 8-Jul-2021.)
Assertion
Ref Expression
df3o2 3o = {∅, 1o, 2o}

Proof of Theorem df3o2
StepHypRef Expression
1 df-3o 8095 . 2 3o = suc 2o
2 df2o3 8108 . . . 4 2o = {∅, 1o}
32uneq1i 4134 . . 3 (2o ∪ {2o}) = ({∅, 1o} ∪ {2o})
4 df-suc 6191 . . 3 suc 2o = (2o ∪ {2o})
5 df-tp 4564 . . 3 {∅, 1o, 2o} = ({∅, 1o} ∪ {2o})
63, 4, 53eqtr4i 2854 . 2 suc 2o = {∅, 1o, 2o}
71, 6eqtri 2844 1 3o = {∅, 1o, 2o}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1528  cun 3933  c0 4290  {csn 4559  {cpr 4561  {ctp 4563  suc csuc 6187  1oc1o 8086  2oc2o 8087  3oc3o 8088
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2793
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-v 3497  df-dif 3938  df-un 3940  df-nul 4291  df-pr 4562  df-tp 4564  df-suc 6191  df-1o 8093  df-2o 8094  df-3o 8095
This theorem is referenced by:  clsk1indlem4  40274  clsk1indlem1  40275
  Copyright terms: Public domain W3C validator