let z1, z2 be set ; :: thesis: ( ( for y1, y2, y3, y4 being set st x = [y1,y2,y3,y4] holds
z1 = y3 ) & ( for y1, y2, y3, y4 being set st x = [y1,y2,y3,y4] holds
z2 = y3 ) implies z1 = z2 )
assume that
A6: for y1, y2, y3, y4 being set st x = [y1,y2,y3,y4] holds
z1 = y3 and
A7: for y1, y2, y3, y4 being set st x = [y1,y2,y3,y4] holds
z2 = y3 ; :: thesis: z1 = z2
z1 = x3 by A1, A6;
hence z1 = z2 by A1, A7; :: thesis: verum