Suppose x ex X. Then (11) proves (14), (14) proves (15), and (12, 15) prove (16).
(11) for allxfor ally(x ex Yeuivalentfor somez(z cont x & z emb Y))

(12) for allxfor ally(x = yeuivalentfor somez(z cont x & z cont y))

(14) for somez(z cont x & z emb X)

(15) for somez(z cont x & z cont x))

(16) x = x

So if x ex X, x = x.