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 Th142:
  x <> y & x <> w & x <> z implies
  ((x,y,w,z) --> (a,b,c,d)).x=a
proof
  assume that
A1: x<>y and
A2: x<>w and
A3: x<>z;
  set f=(x,y) --> (a,b),g=(w,z) --> (c,d);
A4: f.x=a by A1,Th63;
  dom g = {w,z} by Th62; then
A5: not x in dom g by A2,A3,TARSKI:def 2;
  thus thesis by A4,A5,Th11;
end;
