reserve X,X1,X2,Y,Y1,Y2 for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,g1,g2,h for Function,
  R,S for Relation;

theorem Th75:
  X c= dom R implies X c= R"(R.:X)
proof
  assume
A1: X c= dom R;
  let x be object;
  assume
A2: x in X;
  then consider Rx being object such that
A3: [x,Rx] in R by A1,XTUPLE_0:def 12;
  Rx in R.:X by A2,A3,RELAT_1:def 13;
  hence thesis by A3,RELAT_1:def 14;
end;
