Every relation that is transitive and irreflexive is asymmetrical. |
A relation on a set is irreflexive provided that no element is related to itself. |
Every asymmetrical relation is irreflexive. |
The argument is that without distinct individuals that are metaphysically prior to the relations, there is nothing to stand in the irreflexive relations that are supposed to confer individuality on the relata. |
But it is not irreflexive either, since 1 is related to itself. |