i-adjective
unshakable; immovable; undeniable
Describes facts, evidence, beliefs, or resolve that cannot be moved or disputed. Often used with nouns like 事実, 証拠, 信念.
彼のアリバイは動かしがたい事実だ。
His alibi is an unshakable fact.
動かしがたい証拠が提出された。
Undeniable evidence was presented.
揺るがない is more about emotional or mental steadfastness, while 動かしがたい emphasizes objective immovability or indisputability.
Compound of 動かす (to move) in its continuative form 動かし + 難い (hard to do), literally 'hard to move'.