Metamath Proof Explorer

Theorem tpass

Description: Split off the first element of an unordered triple. (Contributed by Mario Carneiro, 5-Jan-2016)

Ref Expression
Assertion tpass 
|- { A , B , C } = ( { A } u. { B , C } )

Proof

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