R function for extracting F-test P-value from linear model object

I thought it would be trivial to extract the p-value on the F-test of a linear regression model (testing the null hypothesis R²=0). If I fit the linear model: fit<-lm(y~x1+x2), I can't seem to find it in names(fit) or summary(fit). But summary(fit)$fstatistic does give you the F statistic, and both degrees of freedom, so I wrote this function to quickly pull out the p-value from this F-test on a lm object, and added it to my R profile. If there's a built-in R function to do this, please comment!