in most any textbook on axiomatic set theory. As you can see, there's no need for explicit mention of the empty set.
The key here is to recognize that it's a hypothetical statement.
(Note: 'e' denotes set membership; the other symbols should be obvious).
(x)(y)(z) [[(xeA ^ yeA) ^ ~(x = y)] -> [zeA -> [(z = x) V (z = y)]]]