reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;
reserve A,B for set;
reserve x,y,i,j,k for object;
reserve x for set;
reserve x for object;
reserve A1,A2,B1,B2 for non empty set,
  f for Function of A1,B1,
  g for Function of A2,B2,
  Y1 for non empty Subset of A1,
  Y2 for non empty Subset of A2;
reserve a,b,c,x,y,z,w,d for object;

theorem
  rng((a,b,c) --> (x,y,z)) c= {x,y,z}
  proof
A1: {x,y} \/ {z} = {x,y,z} by ENUMSET1:3;
A2: rng((a,b,c) --> (x,y,z)) c= rng((a,b) --> (x,y)) \/ rng(c .--> z)
    by Th17;
A3: rng(c .--> z) = {z} by FUNCOP_1:8;
    rng((a,b) --> (x,y)) c= {x,y} by Th62;
    then rng((a,b) --> (x,y)) \/ rng(c .--> z) c= {x,y} \/ {z}
    by A3,XBOOLE_1:13;
    hence thesis by A2,A1;
  end;
