Mutate with nested ifesle

I do get the wrong result, what am I doing wrong?

df <- data.frame(x=c(1,1,NA),y=c(1,NA,NA),z=c(NA,NA,NA))
df <-mutate(df,result=ifelse(is.na(x),NA,ifelse(any(!is.na(y),!is.na(z)),1,0)))

I get this (data[2,4]==0)

   x  y  z result
1  1  1 NA      1
2  1 NA NA      1
3 NA NA NA     NA

Instead of this:

df_wanted <- data.frame(x=c(1,1,NA),y=c(1,NA,NA),z=c(NA,NA,NA), result=c(1,0,NA))

   x  y  z result
1  1  1 NA      1
2  1 NA NA      0
3 NA NA NA     NA