let x1, x2, x3, y1, y2, y3 be set ; :: thesis: ( [x1,x2,x3] = [y1,y2,y3] implies ( x1 = y1 & x2 = y2 & x3 = y3 ) )
assume A1: [x1,x2,x3] = [y1,y2,y3] ; :: thesis: ( x1 = y1 & x2 = y2 & x3 = y3 )
then [x1,x2] = [y1,y2] by ZFMISC_1:27;
hence ( x1 = y1 & x2 = y2 & x3 = y3 ) by A1, ZFMISC_1:27; :: thesis: verum