他tā证zhèng明míng了liǎo自zì己jǐ的de能néng力lì。

He proved his ability.

我wǒ需xū要yào一yì张zhāng证zhèng明míng。

I need a certificate.

事shì实shí证zhèng明míng她tā是shì对duì的de。

The facts prove she was right.

请qǐng你nǐ证zhèng明míng这zhè是shì真zhēn的de。

Please prove that this is true.

数shù据jù证zhèng明míng了liǎo他tā的de理lǐ论lùn。

The data proved his theory.