reserve I for set,
  x,x1,x2,y,z for set,
  A for non empty set;
reserve C,D for Category;
reserve a,b,c,d for Object of C;
reserve f,g,h,i,j,k,p1,p2,q1,q2,i1,i2,j1,j2 for Morphism of C;
reserve f for Morphism of a,b,
        g for Morphism of b,a;
reserve g for Morphism of b,c;
reserve f,g for Morphism of C;

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;
