let x be set ; :: according to FUNCT_1:def 1 :: thesis: for y1, y2 being set st [x,y1] in Y | f & [x,y2] in Y | f holds
y1 = y2
let y1, y2 be set ; :: thesis: ( [x,y1] in Y | f & [x,y2] in Y | f implies y1 = y2 )
assume ( [x,y1] in Y | f & [x,y2] in Y | f ) ; :: thesis: y1 = y2
then ( [x,y1] in f & [x,y2] in f ) by RELAT_1:def 12;
hence y1 = y2 by Def1; :: thesis: verum