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Yes, he could be convicted based upon her testimony alone. While the Bible holds that there has to be at least 2 witnesses to a crime to convict, US Federal (and every state in the US) say that someone can be convicted even based upon a single witness or the victim's testimony.
Now where there are no other witnesses, the testimony of the sole witness / victim would need to be "credible" and is subject to attack on credibility, but assuming that the jury finds, beyond a reasonable doubt, that the defendant committed the crime, then that would hold up.
The key would be to inject a "reasonable doubt" into the situation (such as showing bias, credibility issues, holes in the story, ways the story has changed over time, or conversely, ways the story has stayed the exact same (as that would indicate fabrication and rehearsal), differing accounts given to friends, family members, etc..., as well as alibis for the defendant).
But assuming that the jury believes the victim, even the testimony of that victim would be enough to convict.
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