P-Product Metric on Real Vector Space is Metric/Proof 2

Theorem
The general Euclidean metrics are metrics.

Proof
It can be noted that the general Euclidean metrics are special cases of the product space metrics $d_1, d_2, \ldots, d_\infty$.

Therefore, from Product Space Metrics are Metrics, it can be deduced that the general Euclidean metrics are metrics.