Theorem df2o2 4147

Description: Expanded value of the ordinal number 2.

Assertion

Ref	Expression
df2o2	|- 2o = {(/), {(/)}}

Proof of Theorem df2o2

Step	Hyp	Ref	Expression
1		df-2o 4140	. 2 |- 2o = suc 1o
2		df-suc 2960	. 2 |- suc 1o = (1o u. {1o})
3		df1o2 4146	. . . 4 |- 1o = {(/)}
4	3	sneqi 2422	. . . 4 |- {1o} = {{(/)}}
5	3, 4	uneq12i 2185	. . 3 |- (1o u. {1o}) = ({(/)} u. {{(/)}})
6		df-pr 2417	. . 3 |- {(/), {(/)}} = ({(/)} u. {{(/)}})
7	5, 6	eqtr4 1501	. 2 |- (1o u. {1o}) = {(/), {(/)}}
8	1, 2, 7	3eqtr 1502	1 |- 2o = {(/), {(/)}}

Syntax hints:   = wceq 958   u. cun 2048  (/)c0 2283  {csn 2413  {cpr 2414  suc csuc 2956  1oc1o 4134  2oc2o 4135

This theorem is referenced by:  2dom 4433  pw2en 4452  1sdom2 4531  xp2cda 4940

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-v 1815  df-dif 2052  df-un 2053  df-nul 2284  df-sn 2416  df-pr 2417  df-suc 2960  df-1o 4139  df-2o 4140

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