defpred S₁[ set , set ] means ( $1 in X & [$1,$2] in R );
consider P being Relation such that
A1: for x, y being set holds
( [x,y] in P iff ( x in dom R & y in rng R & S₁[x,y] ) ) from RELAT_1:sch 1();
take P ; :: thesis: for x, y being set holds
( [x,y] in P iff ( x in X & [x,y] in R ) )
let x, y be set ; :: thesis: ( [x,y] in P iff ( x in X & [x,y] in R ) )
( x in X & [x,y] in R implies ( x in dom R & y in rng R ) ) by Def4, Def5;
hence ( [x,y] in P iff ( x in X & [x,y] in R ) ) by A1; :: thesis: verum