Metamath Proof Explorer


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 }