How does Excel evaluate "A1<=A2<=A3"?

I assume Excel evaluates it as (A1<=A2)<=A3,
where "(A1<=A2)" results in the boolean value
TRUE or FALSE.

When I put =(A1<=A2) into C1 and =C1*2 into
C2, C2 is 2 when A1<=A2 and 0 when A1A2. So
I infer that TRUE=1 and FALSE=0 in a numerical
expression.

But =(A1<=A2)<=A3 always evaluates to FALSE,
and =A1<=(A2<=A3) always evaluates to TRUE,
no matter what numerical value I put into A3
(esp. 0) and what the relationship is between
A1 and A2.

The formula =(A1<=A2)<=A3 does behave as
expected if A3 is FALSE. That is, the formula
result is FALSE when A1A2, and it is TRUE
when A1<=A2.

But since =(A1<=A2)*2 has a numerical result
-- ergo, "(A1<=A2)" is treated as a number
sometimes -- shouldn't =(A1<=A2)<=A3 treat
"(A1<=A2)" as a number when A3 is a number?