Is $d(x, y)={(\sum_{i=1}^{n}{|{x_i} -{y_i}|}^p})^{1/p}$ , $x, y\in\mathbb{R^n}$, $0<p<1$ metric on $\mathbb{R^n}$?

Question

$X=\mathbb{R^n}$

Define , $d:X×X\rightarrow\mathbb{R}$ by

$d(x, y)={(\sum_{i=1}^{n}{|{x_i} -{y_i}|}^p})^{1/p}$ , $x, y\in\mathbb{R^n}$, $0<p<1$

Question: Is $d$ a metric on $\mathbb{R^n}$?

Property : (1) Non-negativitiy (2) Definiteness (3) Symmetry holds.

But, Since $0<p<1$ , hence we can't use Holder, Minkowski inequality. So, how can we prove triangle inequality?

Is there any inequality( like Minkowski that helps us to prove triangle inequality of $p-norm$ for $p\ge 1$) which helps us to prove triangle inequality for $0<p<1$.

Please give me hints to prove triangle inequality of $d$? I can't able to proof triangle inequality.