No, as has been explained to you a few times, it is evidence of one of the mechanisms of evolution. At the time of the research, that mechanism was in doubt and there were several different possible explanations. The research falsified a few of them and confirmed the mechanism that was responsible. That was all it was intended to do.
The evidence that leads to the conclusion of common ancestry comes from several other independent lines of evidence.
You can read about those independent lines of evidence here:
http://www.talkorigins.org/faqs/comdesc/
You will notices that none of this rests on the peppered moths study. It is not used to come to the conclusion of common ancestry. Each conclusion is supported by evidence, well referenced, and provides the line of reasoning that would falsify it.
[size=-1]Now if we look again at your original claim:
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How many times have we shown that the peppered moths story is not evidence for evolution and demonstrated that the claims made about the moths have been thoroughtly discredited, and yet it persists to be used by TE's
Can you show us how the claims made about the moths have been discredited or will you withdraw your claim?