select rows with identical columns from a data frame

I have a data frame with several columns.
I want to select the rows with no NAs (as with complete.cases)
and all columns identical.
E.g., for

--8<---------------cut here---------------start------------->8---

f <- data.frame(a=c(1,NA,NA,4),b=c(1,NA,3,40),c=c(1,NA,5,40))
f

    a  b  c
1  1  1  1
2 NA NA NA
3 NA  3  5
4  4 40 40
--8<---------------cut here---------------end--------------->8---

I want the vector TRUE,FALSE,FALSE,FALSE selecting just the first
row because there all 3 columns are the same and none is NA.

thanks!