Suppose Art attacks Bob. Under many circumstances, Bob would have the right to defend himself with force. If charged with a crime, he would claim self-defense. (An example of the ways in which self-defense rules can be complicated is the duty in some jurisdictions to take an opportunity to safely retreat before using force.)
Now suppose Art attacks Bob, and Carl jumps to Bob’s defense. If Carl forcefully repels Art in order to save Bob, and the prosecution later charges Carl with assault, does he have a defense?
He very well might—not because of the self-defense doctrine per se, but due to the concept of defense of others.
Although it involves a different person doing the defending and the rules for it depend on the jurisdiction, defense of others is very similar to self-defense. For either defense to apply in most states, the defendant must reasonably believe that someone is in imminent danger of harm. In addition, the defendant must use only as much force as a reasonable person would use to put an end to the threat.