let D be non empty set ; :: thesis: for z being Element of 2 -tuples_on D ex d1, d2 being Element of D st z = <*d1,d2*>
let z be Element of 2 -tuples_on D; :: thesis: ex d1, d2 being Element of D st z = <*d1,d2*>
z in 2 -tuples_on D ;
then z in { <*d1,d2*> where d1, d2 is Element of D : verum } by Th119;
hence ex d1, d2 being Element of D st z = <*d1,d2*> ; :: thesis: verum