let x, y be set ; {[x,y]} is Relation-like
let a be set ; RELAT_1:def 1 ( a in {[x,y]} implies ex y, z being set st a = [y,z] )
assume
a in {[x,y]}
; ex y, z being set st a = [y,z]
then
a = [x,y]
by TARSKI:def 1;
hence
ex y, z being set st a = [y,z]
; verum