Let $E$ be a (right) Hilbert module over the $C^*$-algebra $B$. Let $\phi$ be a state on the $C^*$-algebra $B$. Then consider $$N_\phi:= \{x \in E: \phi(\langle x,x\rangle)=0\}.$$

I want to show that $N_\phi$ is a submodule of $E$, but for this I need to show that $$b \in B, x \in N_\phi \implies \phi(b^*\langle x,x\rangle b)=\phi(\langle xb,xb\rangle)= 0.$$

Why is this true?