let y, z be object ; :: thesis: for X being set st z in [:X,{y}:] holds
( z `1 in X & z `2 = y )
let X be set ; :: thesis: ( z in [:X,{y}:] implies ( z `1 in X & z `2 = y ) )
assume A1: z in [:X,{y}:] ; :: thesis: ( z `1 in X & z `2 = y )
then z `2 in {y} by Th4;
hence ( z `1 in X & z `2 = y ) by A1, Th4, TARSKI:def 1; :: thesis: verum