$P$ and $Q$ are ideals of ring $R$, $\phi: R \rightarrow R/P \oplus R/Q$, determine $\ker \phi$

Question

$P$ and $Q$ are ideals of ring $R$. To determine $\ker\phi$ of $\phi: R \rightarrow R/P \oplus R/Q$, did not understand a step:

$\ker(\phi) = \{x\in R: \phi (x)=(0,0)\} = \{x\in R: (x+P,x+Q)=(0,0)\}=\{x\in R: x\in P\cap Q\}$.

So did not understand the last step. Thanks and appreciate a hint.