在…下
under …; with …: the condition that makes it possible
Structure
在 条件（帮助／推动／情况） 下 ， 结果
What it means
Under …; with …: names the condition, help or influence that makes the main event possible.
How it is built
在 + (someone's) abstract noun + 下，result: 在老师的帮助下，他的发音进步很快 (With the teacher's help, his pronunciation improved fast). Nouns: 帮助, 支持, 领导, 影响, 压力, 情况, 条件.
When to use it
Neutral to formal. Siblings: 在…上 (in terms of: 在学习上), 在…中 (in the course of: 在讨论中), 在…看来 (in the view of).
Watch out
The slot needs an abstract noun, not just a person: ✗ 在老师下 ✓ 在老师的帮助下. Don't drop 下: ✗ 在大家的支持，我们成功了 ✓ 在大家的支持下，我们成功了.
Examples
在邓小平的推动下，中国开始了改革开放。
At Deng Xiaoping’s urging, China began reform and opening up.
在老师的帮助下，他的发音进步很快。
With the teacher’s help, his pronunciation improved fast.
Learn this in Lesson 51 · HSK 6: 改革开放 (Reform and opening up)
A dialogue, a reading, word cards with audio and a drill that uses it, in Learn Chinese with Bao. This lesson is free.
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