Change of Index Variable of Product

Theorem

 * $\displaystyle \prod_{R \left({i}\right)} a_i = \prod_{R \left({j}\right)} a_j$

where $\displaystyle \prod_{R \left({i}\right)} a_i$ denotes the product over $a_i$ for all $i$ that satisfy the propositional function $R \left({i}\right)$.