Theorem df3o2

Description: Ordinal 3 is the unordered triple containing ordinals 0, 1, and 2. (Contributed by RP, 8-Jul-2021)

	Ref	Expression
Assertion	df3o2	⊢ 3o = { ∅ , 1o , 2o }

Proof

Step	Hyp	Ref	Expression
1		df-3o	⊢ 3o = suc 2o
2		df2o3	⊢ 2o = { ∅ , 1o }
3	2	uneq1i	⊢ ( 2o ∪ { 2o } ) = ( { ∅ , 1o } ∪ { 2o } )
4		df-suc	⊢ suc 2o = ( 2o ∪ { 2o } )
5		df-tp	⊢ { ∅ , 1o , 2o } = ( { ∅ , 1o } ∪ { 2o } )
6	3 4 5	3eqtr4i	⊢ suc 2o = { ∅ , 1o , 2o }
7	1 6	eqtri	⊢ 3o = { ∅ , 1o , 2o }