An Inconsistent pricing strategy is a self financing strategy $\phi$ with $V_T(\phi)= 0$ and $V_0(\phi) \neq 0$
A strong arbitrage is a self-financing strategy $\phi$ with $V_0(\phi) = 0$ and $V_T(\phi) > 0$
Suppose there exists an Inconsistent pricing strategy. Prove from the definition that there must exist a strong arbitrage.
Attempted proof - Let $\phi$ be a self-financing strategy such that $V_0(\phi)\neq 0$ and $V_T(\phi) = 0$.
I am confused how this is possible to prove seems like we have a direct contradiction. Any suggestions are greatly appreciated.