Number of Partitions with no Multiple of 3 equals Number of Partitions where Parts appear No More than Twice

Theorem
Let $n \in \Z_{>0}$ be a (strictly) positive integer.

Let $\map t n$ denote the number of ways $n$ can be partitioned into parts which are specifically not multiples of $3$.

Let $\map v n$ denote the number of ways $n$ can be partitioned such that no part appears twice.

Then:
 * $\forall n \in \Z_{>0}: \map t n = \map v n$