(CBS News) A former college professor's testimony has rocked the murder trial of George Zimmerman. The professor testified Wednesday that Zimmerman got an "A" in his criminal justice class -- a course in which self defense and Florida's "Stand Your Ground" law, now pivotal in Zimmerman's case -- were discussed.
The testimony is important because last year, Zimmerman -- a neighborhood watch volunteer who shot and killed unarmed 17-year-old Trayvon Martin -- said he didn't know about Florida's "Stand Your Ground" law.
CBS News legal analyst Jack Ford said it could be an assist for the prosecution, explaining on "CBS This Morning," "At its core, this case is about George Zimmerman's credibility. Usually, as you know, a defendant has no obligation to prove anything in a criminal case except if you introduce a defense of self-defense. Then there is an obligation for a defendant to come forward with some degree of proof. And this case is about what version the jury wants to accept.
"If they accept the prosecution's version that George Zimmerman was the instigator, well then he can't rely on self-defense," Ford continued. "You can't start a fight and say, 'You know what? I'm not doing well here, I'm going to get my gun and blow this guy away.' If they accept George Zimmerman's version, that Trayvon Martin was the instigator and he had a reasonable fear for his safety, then self-defense can work. So credibility is so important."
The college professor may prove important here, Ford explained, because the prosecution is going to impress on the jury the alleged discrepancy between what Zimmerman said he didn't know and what the professor says Zimmerman knew. Ford added, "The prosecution is going to say to the jurors, 'You can't believe (him).' Jurors are told by judges that if they find that a witness didn't tell the truth about something, they can choose to disregard everything that witness says if they want to. They're also told they can choose to say, 'OK, didn't tell the truth about one thing, but we still believe him about everything else.' This could be a very important witness for the prosecution depending upon how the jury views it."
The evidence in the case -- including DNA evidence presented in the trial -- may also support the prosecution's case. Ford called the DNA "window dressing" that many jurors may expect as a result of what he called the "'CSI'-effect," but it may also question Zimmerman's credibility. Ford said, "George Zimmerman has said, 'Trayvon Martin was reaching for my gun, I got it first, and had to use it.' Although one of his friends said he told him that Trayvon Martin grabbed the gun. This evidence saying there was no DNA of Trayvon Martin on the gun -- it again goes the credibility of George Zimmerman, and as I said before that's the core here. Ultimately, what is the jury going to think and whose version are they going to accept."
Another interesting aspect of the case, according to Ford, is that the judge has ruled George Zimmerman's past is fair game, including the fact that he applied to be a police officer. "Usually, a case is tried on the facts of that case alone -- you can't go into other things beforehand, but here the prosecution's theory is George Zimmerman was a wannabe cop," Ford said. "The prosecution is claiming that's his motivation for initiating this conflict here with Trayvon Martin. So again, it could be something that could be helpful to the prosecution."
For more on the case, watch Ford's full analysis in the video above.