Bayes Theorem for Conditional event that is an intersection of independent events. I have a question regarding Bayes theorem, and independent intersected events as the conditional.  How can this probability be decomposed using Bayes?

$P(H \mid E \cap R)$ where $E$ and $H$ are independent events. 

Does that equal $P(H\mid E)\cdot P(H\mid R)$?
$P(H|E,R) = P(H,E,R)/P(E,R)$

$ P(H,E,R) = P(H|E,R)/P(E,R)$
$P(H|E,R) = P(H,E,R)/P(E,R)$

$ P(H,E,R) = P(H|E,R)/P(E,R)$