Theorem tpcoma

Description: Swap 1st and 2nd members of an unordered triple. (Contributed by NM, 22-May-2015)

	Ref	Expression
Assertion	tpcoma	|- { A , B , C } = { B , A , C }

Proof

Step	Hyp	Ref	Expression
1		prcom	|- { A , B } = { B , A }
2	1	uneq1i	|- ( { A , B } u. { C } ) = ( { B , A } u. { C } )
3		df-tp	|- { A , B , C } = ( { A , B } u. { C } )
4		df-tp	|- { B , A , C } = ( { B , A } u. { C } )
5	2 3 4	3eqtr4i	|- { A , B , C } = { B , A , C }