Re: Directed graph connectedness - simple?

Victor Porton wrote:
I've found myself already several hours attempting
to prove seemingly obvious statement:

A directed graph (Vertices,Edges) is connected
if and only if
$(A\times B)\cap Edges \ne \emptyset$
for any two nonempty sets $A$ and $B$ such that
$A\cup B\supseteq Vertices$.

I'm especially interested in the reverse implication.
(I've already proved the direct implication.)

Note that saying "connected" I meant "strongly connected".

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