reserve x,x1,x2,y,y9,y1,y2,z,z1,z2 for object,P,X,X1,X2,Y,Y1,Y2,V,Z for set;
reserve A for set,
  f,g,h for Function;

theorem Th77:
 for x,y,z being object holds
  f tolerates g & [x,y] in f & [x,z] in g implies y = z
proof let x,y,z be object;
  set h = f \/ g;
  assume f tolerates g;
  then
A1: h is Function by Th51;
  assume [x,y] in f & [x,z] in g;
  then [x,y] in h & [x,z] in h by XBOOLE_0:def 3;
  hence thesis by A1,FUNCT_1:def 1;
end;
