If A implies B (A -> B) then you cannot have A -> C Unless you meant it can imply both, but then still A implies B. A dog (A) has 4 legs(B). Something that

If A implies B (A -> B) then you cannot have A -> C Unless you meant it can imply both, but then still A implies B. A dog (A) has 4 legs(B). Something that does not have 4 legs (not B) is not a dog (not A). A cow though (not A) could still have 4 legs