How to prove: If $\textsf{EXP} \subseteq \textsf{P/poly} $ then $\textsf{EXP} = \Sigma^p_2$
The more classical statement is that if $\textsf{EXP} \subseteq \textsf{P/poly}$ then $\textsf{EXP} = \textsf{MA}$, due to Babai, Fortnow and Lund. Impagliazzo, Kabanets and Wigderson showed that $\textsf{NEXP} \subseteq \textsf{P/poly}$ iff $\textsf{NEXP} = \textsf{MA}$. See lecture notes of Bogdanov for proof sketches.