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!

	# Function to extract the overall ANOVA p-value out of a linear model object
	lmp <- function (modelobject) {
	if (class(modelobject) != "lm") stop("Not an object of class 'lm' ")
	f <- summary(modelobject)$fstatistic
	p <- pf(f[1],f[2],f[3],lower.tail=F)
	attributes(p) <- NULL
	return(p)
	}
	# simulate some data
	set.seed(42)
	n=20
	d=data.frame(x1=rbinom(n,2,.5), x2=rbinom(n,2,.5))
	d=transform(d, y=x1+x2+rnorm(n))
	#fit the linear model
	fit=lm(y ~ x1 + x2, data=d)
	summary(fit) #shows that the F-test is 0.006641
	names(summary(fit)) #can't access that p-value using this!
	names(fit) # this doesn't work either
	lmp(fit) # uses the above function to capture the F-test p-value.

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