One new and additional detail given by Peter is the phrase, through which you and all your household will be saved.
This confirms that the real issue at hand was not the food laws or any kind of defilement from association with Gentiles, but the salvation of God’s elect (see Acts 2:39).1 The salvation of God’s chosen people was the very purpose of Jesus’ ministry (Luke 19:40) and of the proclamation of the apostles (Acts 2:21, Acts 2:40).2
13 And he told us how he had seen the angel stand in his house and say, ‘Send to Joppa and bring Simon who is called Peter;