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 Th135:
  (b <> c implies ((a,b,c) --> (x,y,z)).b = y) &
  ((a,b,c) --> (x,y,z)).c = z
  proof
    set f = (a,b) --> (x,y);
    set g = c .--> z;
    set h = (a,b,c) --> (x,y,z);
A1: c in {c} by TARSKI:def 1;
A2: dom g = {c};
   hereby assume b <> c;
    then
A3: not b in {c} by TARSKI:def 1;
    thus h.b = f.b by A3,A2,Th11
    .= y by Th63;
   end;
    thus h.c = g.c by A1,A2,Th13
    .= z by FUNCOP_1:72;
  end;
