Transformation of queries with NOT IN predicands into queries with anti-joins

A query of the form
SELECT * FROM t1 WHERE P1(t1) AND t1.a NOT IN (SELECT t2.a FROM t2 WHERE P2(t2,t1)
can be transformed into the equivalent query
SELECT * FROM t1 LEFT JOIN ON t1.a=t2.a AND P2(t2,t1) WHERE P1(t1)
if t1.a is not nullable.

After transformation a hash join algorithm can be employed when there is no indexes matching t2.a