Holding one down does not lift another up. Letting one person rise tends to improve the lives of others.
"Poverty" is a much-abused and much-redefined word. Many rely on an expansive legal definition intended to include as many as possible. Consider that the USA definition of "poverty line" sets some 87% of the world's population as "poor", which is a practical absurdity clouded by emotion.
Using an objective definition of "poor" focused on one's sustenance (and unaffected by whether someone else is very comfortable) we find that, indeed, world "poverty" is declining substantially. A greater percentage of world population than ever is able to obtain more than sufficient nutrition, shelter, etc to live indefinitely - to wit, aren't "poor".
And yes, if someone can improve their income/wealth to a great degree, they are most likely improving the well-being of others in the process. For capitalism to be indefinitely self-sustaining, both parties in a transaction must benefit from the transaction in an economically sustainable manner. This persistent meme of the wealthy sucking the rest of society to death is absurd, as killing customers (or otherwise rendering their income negligible) is very bad for business. Yes, wealth inequality can help eradicate poverty by giving some a reason to improve the lives of others; total wealth equality (especially when forced by government) means nobody has reason to improve themselves relative to others, consequently institutionalizing poverty as the socioeconomic norm.