Dominance in Data Envelopment analysis in R

I need to formalise in R the following rule, called dominance:

(x1,y1) dominates (x2,y2) if and only if x1<=x2(1) and y1>=y2(2) and (x1,y1) different from (x2,y2)(3).

x and y are vectors containing several variables. I have tried the following:

i1 = (min(x1)<=min(x2) && max(y1)>=max(y2))

where i1 is a boolean which will give me a TRUE if x1 dominates x2 indeed, a FALSE if not.

However I struggle to implement (3), which is when 1 and 2 are equal for both x and y.