Two moral values exist, such that one implies the other. Example: "One should be nice" -> "One should not kill". Do two moral values exist, such that both imply the other? Would two such moral values be exactly equal, making a differentiation of the morals meaningless?
That's an excellent question and I don't know of any article or other reference about it. AFAIK, there should be such two values, although in the end it all hinges on what you call a value and whether you think that the use of implications is appropriate in this context. Why should there be such pairs of values?
Take any common variety of goodness like e.g. medical goodness or hedonic goodness, and a statement like (1) that can be read in that way:
(1) This apple is good.
Then it seems that we should be able to give explanations like (1) means
(2) This apple is healthy for you right now.
(3) This apple gives me pleasure right now.
But this, it seems, essentially means that something is good in the medical sense of 'good' if and only if it is healthy to you, and that something is good in the hedonic sense of 'good' if and only if it gives you pleasure. So here you have your biconditionals.
However, there are numerous problems with this view. One of them is that one could argue that it confuses synonymy with explication. Logical positvists like Carnap and Ayer were careful to keep the two apart and not to conflate explication with statements of synonmy. Perhaps the biconditional (in the sense of "material implication in both directions") is not the right way to think about problems of value equivalence. Still, any intuitively understandable variety of goodness should have a corresponding explanation that can (to some extent) be substituted for it.
Another problem is whether you are willing to call different meanings of "good" values at all - "good" seems to be a very special case. Perhaps it always combines different (real, underlying) values as a sort of shortcut.
i'm not sure what you mean, but i can't "comment" so will "answer".
of course if i ought not kill homo sapiens i ought not kill humans... likewise if i am obliged to honour my mother and father then i am obliged to honour mr and mrs user [and visa versa]; this is a less trivial moral equivalence.
being nice and not killing, could be one and is more interesting because it seems that being nice does not necessarily contain not murdering... and if that can be shown, that it is possible to be a nice murderer [or to murder nicely], then it seems to me that they cannot strictly imply each other.
we might also ask: what about other forms of inference? perhaps i can justify the claim that murder is not nice by confirming all the cases of nasty murders; then even if a nice murder is only contingently impossible it is still so [and we can go the other way too: all the nice deeds that aren't murders].
so it seems to me that yes obligations can entail each other - by a priori, or by a posteriori necessity, or by less strict inference.
which may go some way to answering your question, at least the best I can do without knowing why you ask