Metamath Proof Explorer

Theorem tpcomb

Description: Swap 2nd and 3rd members of an unordered triple. (Contributed by NM, 22-May-2015)

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

Proof

Step Hyp Ref Expression
1 tpcoma 
 |-  { B , C , A } = { C , B , A }
2 tprot 
 |-  { A , B , C } = { B , C , A }
3 tprot 
 |-  { A , C , B } = { C , B , A }
4 1 2 3 3eqtr4i 
 |-  { A , B , C } = { A , C , B }