Since

means the left-hand side is stronger (or in this case as strong as and thus equivalent) than the right-hand side.

Thus the left-hand side implies the right-hand side: whenever the left-hand side is true, the right-hand side is true, but vice versa is not necessary the case (except in examples like this when there is actually a logical equivalence between the left- and right-hand side).

If I were to write a

in stead of the

, the truth tables would lead me to the conclusion this is always a tautology. Right?