Is this triangle inequality correct?

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I'm reading a book of Calculus and in the proof of the sum law of Limits I came across this: "By the triangle inequality, we have $|f(x)-L_1| + |g(x)-L_2| \le |f(x) - L_1 + g(x) - L_2| = |f(x) + g(x) - (L_1 + L_2)|$".

For clarity's sake:

$f: \Bbb R \to \Bbb R\\ \quad\; x \mapsto f(x)$, $g:\Bbb R \to \Bbb R\\ \quad\; x \mapsto g(x)$

And $\lim_{x \to a} f(x) = L_1$, $\lim_{x \to a} g(x) = L_2$

Is it correct? Shouldn't "$\le$" be "$\ge$" in this case?