# Does $E(X \mid Y,Z)=0$ imply $E(X \mid Y)=0$?

Does $$E(X \mid Y,Z)=0$$ imply $$E(X \mid Y)=0$$?

In other words, if we have $$E(X \mid Y,Z)=0$$ then can we also say $$E(X \mid Y)=0$$?

$$\mathbb{E}\left(X\mid Y\right)=\mathbb{E}\left[\mathbb{E}\left(X\mid Y,Z\right)\mid Z\right]=\mathbb{E}\left[0\mid Z\right]=0$$.