create variable based on multiple similar variables in R

My data looks like this:

  zipid1 zipid2 zipid3 zipid4 zipid5 zipid6 zipid7 zipid8 zipid9 zipid10 zipid11 zipid12 zipid13 hospid local
1      0      0      0      0      1      0      0      0      0       0       0       0       0      5     0
2      0      0      1      0      1      0      0      0      0       0       0       0       0      5     0
3      0      0      0      0      0      0      1      0      0       0       0       0       0      5     0
4      0      0      1      0      0      0      0      0      0       0       0       0       0      5     0
5      0      0      1      0      1      0      0      0      0       0       0       0       0      5     0
6      0      0      0      0      1      0      0      0      0       0       0       0       0      5     0

How can I create a local variable = 1 when zipid1 ==1 & hospid =1, zipid2 == 1 & hospid == 2.etc. and else = 0 (ie, zipid = hospid)?

I tried ifelse but did not work well.

for (i in 1:13) {
name = paste0("zipid", i)
local$local <- with(local, ifelse(name == 1 & hospid == i, 1, 0))
}

Thanks!