let Y1, Y2 be set ; :: thesis: ( ( for y being object holds ( y in Y1 iff ex x being object st ( [x,y]in R & x in X ) ) ) & ( for y being object holds ( y in Y2 iff ex x being object st ( [x,y]in R & x in X ) ) ) implies Y1 = Y2 ) assume that A4:
for y being object holds ( y in Y1 iff ex x being object st ( [x,y]in R & x in X ) )
and A5:
for y being object holds ( y in Y2 iff ex x being object st ( [x,y]in R & x in X ) )
; :: thesis: Y1 = Y2