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;
