Of course, some would argue that antibiotic resistant bacteria is not a result of mutation, but rather proliferation of a less dominant bacteria.
It's both. Bacterial genes, as all genes do, will randomly mutate. In some cases this mutation confers resistance to an antibiotic. This trait is heritable since it is based on a change in the genes. This mutation was not caused by the antibiotic and would occur without antibiotics. But with no antibiotic, the trait is not useful.
But in the presence of antibiotics, this mutation now provides an advantage. The bacteria with this mutation are more likely to survive and reproduce more bacteria that also inherit this trait. Over time, the frequency of this heritable trait increases in the population, which is, for those paying attention, precisely the definition of evolution.
Of course those that deny evolution will need to come up with a different explanation. I'm waiting to read if this is because an Intelligent Designer decided we needed some antibiotic resistant bugs for some reason.
