let x1, x2, x3, x4, x5, y1, y2, y3, y4, y5 be set ; :: thesis: ( [x1,x2,x3,x4,x5] = [y1,y2,y3,y4,y5] implies ( x1 = y1 & x2 = y2 & x3 = y3 & x4 = y4 & x5 = y5 ) )
assume [x1,x2,x3,x4,x5] = [y1,y2,y3,y4,y5] ; :: thesis: ( x1 = y1 & x2 = y2 & x3 = y3 & x4 = y4 & x5 = y5 )
then ( [x1,x2,x3,x4] = [y1,y2,y3,y4] & x5 = y5 ) by ZFMISC_1:33;
hence ( x1 = y1 & x2 = y2 & x3 = y3 & x4 = y4 & x5 = y5 ) by MCART_1:33; :: thesis: verum