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 Th134:
  a <> b & a <> c implies ((a,b,c) --> (x,y,z)).a = x
 proof assume that
A1: a <> b and
A2: a <> c;
   not a in dom(c.-->z) by A2,TARSKI:def 1;
  hence ((a,b,c) --> (x,y,z)).a = ((a,b) --> (x,y)).a by Th11
    .= x by A1,Th63;
 end;
