Some examples:

P = PROJECT(a,b) R

If a is a key of R then a is a key of P

If b is a key of R then b is a key of P

Otherwise (a,b) is a key of P

Q = S JOIN T

The union of the key attributes of S and T is a superkey of Q (possibly a candidate key).

Key inference rules exist for all the relational operations. It's just a natural consquence of the closure property, ie: every result is a relation and every relation has at least one key.