let x be set ; :: according to FUNCT_1:def 1 :: thesis: for y1, y2 being set st [x,y1] in id X & [x,y2] in id X holds
y1 = y2
let y1, y2 be set ; :: thesis: ( [x,y1] in id X & [x,y2] in id X implies y1 = y2 )
assume ( [x,y1] in id X & [x,y2] in id X ) ; :: thesis: y1 = y2
then ( x = y1 & x = y2 ) by RELAT_1:def 10;
hence y1 = y2 ; :: thesis: verum