Let
-
and
-
Due to
fact (2),
we have
-
Due to
fact (3),
we have
-
and, because of
fact (1),
we have
-
According to
fact (6),
is perpendicular to and to ; therefore,
-
with some
,
as this orthogonality condition defines a line. Because of
fact (5)
and the condition, we get
-
hence,
-
Using
fact (3),
we obtain
and
.
Altogether we get
and this is the claim.