Change of Index Variable of Summation

Theorem

 * $\displaystyle \sum_{\Phi \left({i}\right)} a_i = \sum_{\Phi \left({j}\right)} a_j$

where $\displaystyle \sum_{\Phi \left({i}\right)} a_i$ denotes the summation over $a_i$ for all $i$ that satisfy the propositional function $\Phi \left({i}\right)$.