How is 役に立った ( helpful ) formed?

My guess is that the phrase is derived from the composition of the following:

1. 役 (yaku) : service, use

2. に：particle for destination

3. 立った：perfective of 立つ (tatsu)

So it's extended meaning like "rise to a supporting role", "being supported".

Am I more or less correct?

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I have read posts:

Is "役立つ" a recent lexicalization of "役に立つ"? Is it less formal?

Difference Between 手伝う, 力になる, and 役に立つ