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Newton merely stated the law of inertia as:

An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

How does it prove the existence of inertial frames? I see no mention of it in the original law.

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Newton's first law doesn't "prove" the existence of inertial frames; it defines inertial frames.

An inertial frame is one in which Newton's first law holds.

Allure
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