Residual finiteness of a free group
= Residual finiteness of a free group
Every finitely generated <free group> is a <residually finite group>. For $F_2$, the <ping-pong lemma> embeds it into $\operatorname{SL}_2(\mathbb Z)$, and <reduction modulo a prime in an integral matrix group> separates each nonidentity element in a finite quotient.