  Mantel's theorem says that among all triangle-free graphs of a given order
the balanced complete bipartite graph is the unique graph of maximum size. We
prove an analogue of this result for 3-graphs. Let $K_4^-=\{123,124,134\}$,
$F_6=\{123,124,345,156\}$ and $\mathcal{F}=\{K_4^-,F_6\}$: for $n\neq 5$ the
unique $\mathcal{F}$-free 3-graph of order $n$ and maximum size is the balanced
complete tripartite 3-graph $S_3(n)$ (for $n=5$ it is
$C_5^{(3)}=\{123,234,345,145,125\}$). This extends an old result of Bollob\'as
that $S_3(n) $ is the unique 3-graph of maximum size with no copy of
$K_4^-=\{123,124,134\}$ or $F_5=\{123,124,345\}$.
