Given $P(G|E_1| E_2)$:
Would it be wrong to say $P(G|[E_1| E_2])=P([G|E_1]| E_2)$ ?
By this I mean considering that $E_1| E_2$ is an event that gives the condition for event $G$ / considering that $E_2$ is an event that gives the condition for event $G|E_1$?
If i could treat it as an event would i be able to say (by the definition of conditional probability)
$$P(G|[E_1| E_2])= \frac{P(G\cap [E_1| E_2])}{P(E_1| E_2)}$$