# Martingale positive price process

I hope you can help me with this problem. In my lecture notes, my professor stated that for a state price deflator $$\phi\in L_{n+1}^2(P, F)$$ (F being a filtration) and a strictly positive price process $$(I_t)_{t\in \{0,...,n\}}$$, $$(\phi_t \cdot I_t)_{t\in \{0,...,n\}}$$ is a (P,F) martingale. How can I prove this?

I know that you can write $$E(\phi_{t+1} I_{t+1}|\mathcal{F}_t)=E(E(\phi_{t+1} I_{t+1}|\mathcal{F}_{t+1})|\mathcal{F}_t)$$. But I do not know how to proceed in order to show that this is equal to $$\phi_t I_t$$. Do you have any hints for me?

I appreciate any kind of help. Thanks a lot.