Here "his arm" is a metonym that stands for God's power. Alternate translation: "shown that he is very powerful" (See: [[rc://en/ta/man/translate/figs-metonymy]])
Here "hearts" is a metonym for people's inner beings. Alternate translation: "who were proud in their thoughts" or "who were proud" (See: [[rc://en/ta/man/translate/figs-idiom]])