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;

theorem Th84:
  for f being Function, a,b,c,d being object st a <> b holds
  (f +* ((a,b)-->(c,d))) .a = c & (f +* ((a,b)-->(c,d))) .b = d
proof
  let f be Function, a,b,c,d be object such that
A1: a <> b;
  set g = (a,b)-->(c,d);
A2: dom g = {a,b} by Th62;
  then a in dom g by TARSKI:def 2;
  hence (f +* g).a = g.a by Th13
    .= c by A1,Th63;
  b in dom g by A2,TARSKI:def 2;
  hence (f +* g).b = g.b by Th13
    .= d by Th63;
end;
