  In 1965 Erd\H os conjectured that for all $k\ge2$, $s\ge1$ and $n\ge k(s+1)$,
an $n$-vertex $k$-uniform hypergraph $\F$ with $\nu(\F)=s$ cannot have more
than \newline $\max\{\binom{sk+k-1}k,\;\binom nk-\binom{n-s}k\}$ edges. It took
almost fifty years to prove it for triple systems. In 2012 we proved the
conjecture for all $s$ and all $n\ge4(s+1)$. Then {\L}uczak and Mieczkowska
(2013) proved the conjecture for sufficiently large $s$ and all $n$. Soon
after, Frankl proved it for all $s$. Here we present a simpler version of that
proof which yields Erd\H os's conjecture for $s\ge33$. Our motivation is to lay
down foundations for a possible proof in the much harder case $k=4$, at least
for large $s$.
