[tr352]

Yes it does. In fact, in classical logic, A->B is equivalent to !B->!A. See https://en.m.wikipedia.org/wiki/Contraposition

[spookyuser]

Exactly.

A consequence of this being true is the Raven Paradox [1], seemingly the OP has solved the classic riddle in a HN thread.

[1] https://en.wikipedia.org/wiki/Raven_paradox