# Interpretation of a 95% confidence interval calculated via bootstrapping?

I've been thinking about what exactly a 95% confidence interval means when it is calculated via bootstrapping.

The formal definition of a 95% confidence interval is something like this: "if the population is repeatedly sampled and a confidence interval is calculated after each sample, then the population parameter being estimated will be included in the confidence interval 95% of the time".

But in bootstrapping, we don't calculate a confidence interval after each resample, we just calculate a single confidence interval at the end of the all of the resamples.

So the formal definition of a 95% confidence interval isn't transferable to a 95% confidence interval calculated via bootstrapping, because we don't calculate a confidence interval after each resample.

So, like Mike Lawrence asked, surely the 95% confidence interval calculated via bootstrapping must be interpreted as this: "there is a 95% probability that the confidence interval contains the population parameter we're trying to estimate". Yes?