therefore; consequently; for that reason
Formal or literary conjunction used to state a logical conclusion based on the preceding statement. Similar to だから but more written and reasoned.
He destroyed all the evidence. Therefore, he cannot escape conviction.
I think, therefore I am.
Because he was poor, he could not go to university.
ゆえに is an even more literary, terse variant of それ故, often seen in written proofs or classical-style writing.
ゆえに is an even more formal, classical-sounding version of よって, common in legal or academic writing.
From the noun 故 (ゆえ, 'reason') + the particle に, literally 'for the reason that'. The kanji 故 carries the meaning of 'cause' or 'reason'.