Conditional expectation and stopping time $\mathbb{E}(X1_{T\leq m}|\mathcal{F}_{T\wedge m})=\mathbb{E}(X1_{T\leq m}|\mathcal{F}_T)$

Question

Let $X$ be a random variable and $T$ a stopping time in a filtrated probability space. If $m > 0$ is it true that: $$\mathbb{E}\left(X1_{T\leq m}|\mathcal{F}_{T\wedge m}\right)=\mathbb{E}\left(X1_{T\leq m}|\mathcal{F}_T\right).$$

I try to do it by the definition of conditional expectation but I didn't get it.

Any help will be appreciated