let x1, x2, x3, x4, x5, x6, x7, y1, y2, y3, y4, y5, y6, y7 be set ; :: thesis: ( [x1,x2,x3,x4,x5,x6,x7] = [y1,y2,y3,y4,y5,y6,y7] implies ( x1 = y1 & x2 = y2 & x3 = y3 & x4 = y4 & x5 = y5 & x6 = y6 & x7 = y7 ) )
assume A1: [x1,x2,x3,x4,x5,x6,x7] = [y1,y2,y3,y4,y5,y6,y7] ; :: thesis: ( x1 = y1 & x2 = y2 & x3 = y3 & x4 = y4 & x5 = y5 & x6 = y6 & x7 = y7 )
then [x1,x2,x3,x4,x5,x6] = [y1,y2,y3,y4,y5,y6] by ZFMISC_1:27;
hence ( x1 = y1 & x2 = y2 & x3 = y3 & x4 = y4 & x5 = y5 & x6 = y6 & x7 = y7 ) by A1, Th45, ZFMISC_1:27; :: thesis: verum