now

let x be set ; :: thesis: ( x in P \/ R implies ex y, z being set st x = [y,z] )
A1: ( x in P implies ex y, z being set st x = [y,z] ) by Def1;
( x in R implies ex y, z being set st x = [y,z] ) by Def1;
hence ( x in P \/ R implies ex y, z being set st x = [y,z] ) by A1, XBOOLE_0:def 3; :: thesis: verum

end;

hence P \/ R is Relation-like by Def1; :: thesis: verum