应许 is the standard Chinese Bible term for divine promises — 应许之地 (yīngxǔ zhī dì, 'the Promised Land') is the fixed phrase for Canaan in Christian translations.
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In modern conversation, prefer 答应 (dāyìng, to agree) or 允许 (yǔnxǔ, to permit). 应许 carries a literary or religious tone.
