Let $G_{1}, G_{2}$ be two profinite groups, and $f: G_{1} \longrightarrow G_{2}$ is an continue injective homomorphism. Let $p$ be a prime number, then we get a pro-p completion $f^{p}: G_{1}^{p} \longrightarrow G_{2}^{p}$.

Is $f^{p}$ an injective homomorphism?