theorem Th44:
  dom p1 = a & dom p2 = a implies (x1,x2)-->(p1,p2) is
  Projections_family of a,{x1,x2}
proof
  assume
A1: dom p1 = a & dom p2 = a;
  doms ((x1,x2)-->(p1,p2)) = (x1,x2) --> (dom p1,dom p2) by Th6
    .= {x1,x2} --> a by A1,FUNCT_4:65;
  hence thesis by Def13;
end;
