let y, z be Element of X5; :: thesis: ( ( for x1, x2, x3, x4, x5 being set st x = [x1,x2,x3,x4,x5] holds
y = x5 ) & ( for x1, x2, x3, x4, x5 being set st x = [x1,x2,x3,x4,x5] holds
z = x5 ) implies y = z )
assume A19: for x1, x2, x3, x4, x5 being set st x = [x1,x2,x3,x4,x5] holds
y = x5 ; :: thesis: ( ex x1, x2, x3, x4, x5 being set st
( x = [x1,x2,x3,x4,x5] & not z = x5 ) or y = z )
assume A20: for x1, x2, x3, x4, x5 being set st x = [x1,x2,x3,x4,x5] holds
z = x5 ; :: thesis: y = z
consider xx1 being Element of X1, xx2 being Element of X2, xx3 being Element of X3, xx4 being Element of X4, xx5 being Element of X5 such that
A21: x = [xx1,xx2,xx3,xx4,xx5] by A1, Th17;
y = xx5 by A21, A19;
hence y = z by A21, A20; :: thesis: verum