  We prove that in either the convergent or overconvergent setting, an
absolutely irreducible $F$-isocrystal on the absolute product of two or more
smooth schemes over perfect fields of characteristic $p$, further equipped with
actions of the partial Frobenius maps, is an external product of
$F$-isocrystals over the multiplicands. The corresponding statement for lisse
$\bar{\mathbb{Q}}_\ell$-sheaves, for $\ell \neq p$ a prime, is a consequence of
Drinfeld's lemma on the fundamental groups of absolute products of schemes in
characteristic $p$. The latter plays a key role in V. Lafforgue's approach to
the Langlands correspondence for reductive groups with $\ell$-adic
coefficients; the $p$-adic analogue will be considered in subsequent work with
Daxin Xu.
