if statement - Type-juggling and (strict) greater/lesser-than comparisons in PHP

PHP is famous for its type-juggling. I must admit it puzzles me, and I'm having a hard time to find out basic logical/fundamental things in comparisons.

For example: If $a > $b is true and $b > $c is true, must it mean that $a > $c is always true too?

Following basic logic, I would say yes however I'm that puzzled I do not really trust PHP in this. Maybe someone can provide an example where this is not the case?

Also I'm wondering with the strict lesser-than and strict greater-than operators (as their meaning is described as strictly which I only knew in the past from the equality comparisons) if it makes any difference if left and right operands are swapped with strictly unequal values:

# Precondition:
if ($a === $b) {

    throw new Exception(
       'Both are strictly equal - can not compare strictly for greater or smaller'
    );
}

($a > $b) !== ($b > $a)

For most of all type comparison combinations these greater / lesser comparison operators are not documented, so reading the manual was not really helpful in this case.