reserve f,g,h for Function,
  A for set;
reserve F for Function,
  B,x,y,y1,y2,z for set;
reserve x,z for object;

theorem Th7:
  x in A implies (A --> z).x = z
proof
  assume
A1: x in A;
  z in {z} by TARSKI:def 1;
  then [x,z] in (A --> z) by A1,ZFMISC_1:87;
  hence thesis by FUNCT_1:1;
end;
