let x1, x2, x3, x4, y1, y2, y3, y4 be object ; :: thesis: ( [x1,x2,x3,x4] = [y1,y2,y3,y4] implies ( x1 = y1 & x2 = y2 & x3 = y3 & x4 = y4 ) )
assume A1: [x1,x2,x3,x4] = [y1,y2,y3,y4] ; :: thesis: ( x1 = y1 & x2 = y2 & x3 = y3 & x4 = y4 )
then [x1,x2,x3] = [y1,y2,y3] by Th1;
hence ( x1 = y1 & x2 = y2 & x3 = y3 & x4 = y4 ) by A1, Th3, Th1; :: thesis: verum