Metamath Proof Explorer

Theorem tpidm23

Description: Unordered triple { A , B , B } is just an overlong way to write { A , B } . (Contributed by David A. Wheeler, 10-May-2015)

Ref Expression
Assertion tpidm23 
|- { A , B , B } = { A , B }

Proof

Step Hyp Ref Expression
1 tprot 
 |-  { A , B , B } = { B , B , A }
2 tpidm12 
 |-  { B , B , A } = { B , A }
3 prcom 
 |-  { B , A } = { A , B }
4 1 2 3 3eqtri 
 |-  { A , B , B } = { A , B }