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 } |
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 } |