Theorem df2o2 4277

Description: Expanded value of the ordinal number 2.

Assertion

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

Proof of Theorem df2o2

Step	Hyp	Ref	Expression
1		df-2o 4270	. 2 |- 2o = suc 1o
2		df-suc 2981	. 2 |- suc 1o = (1o u. {1o})
3		df1o2 4276	. . . 4 |- 1o = {(/)}
4	3	sneqi 2476	. . . 4 |- {1o} = {{(/)}}
5	3, 4	uneq12i 2234	. . 3 |- (1o u. {1o}) = ({(/)} u. {{(/)}})
6		df-pr 2471	. . 3 |- {(/), {(/)}} = ({(/)} u. {{(/)}})
7	5, 6	eqtr4i 1541	. 2 |- (1o u. {1o}) = {(/), {(/)}}
8	1, 2, 7	3eqtri 1542	1 |- 2o = {(/), {(/)}}

Syntax hints:   = wceq 992   u. cun 2097  (/)c0 2332  {csn 2467  {cpr 2468  suc csuc 2977  1oc1o 4264  2oc2o 4265

This theorem is referenced by:  2dom 4568  pw2en 4587  1sdom2 4672  xp2cda 5080

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 998  ax-gen 999  ax-8 1000  ax-10 1002  ax-12 1004  ax-17 1007  ax-4 1009  ax-5o 1011  ax-6o 1014  ax-9o 1159  ax-10o 1177  ax-16 1247  ax-11o 1255  ax-ext 1500

This theorem depends on definitions:  df-bi 145  df-or 222  df-an 223  df-ex 1017  df-sb 1209  df-clab 1506  df-cleq 1511  df-clel 1514  df-v 1858  df-dif 2101  df-un 2102  df-nul 2333  df-sn 2470  df-pr 2471  df-suc 2981  df-1o 4269  df-2o 4270

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