let y, z be Element of X1; :: thesis: ( ( for x1, x2, x3 being set st x = [x1,x2,x3] holds
y = x1 ) & ( for x1, x2, x3 being set st x = [x1,x2,x3] holds
z = x1 ) implies y = z )
assume A3: for x1, x2, x3 being set st x = [x1,x2,x3] holds
y = x1 ; :: thesis: ( ex x1, x2, x3 being set st
( x = [x1,x2,x3] & not z = x1 ) or y = z )
assume A4: for x1, x2, x3 being set st x = [x1,x2,x3] holds
z = x1 ; :: thesis: y = z
consider xx1 being Element of X1, xx2 being Element of X2, xx3 being Element of X3 such that
A5: x = [xx1,xx2,xx3] by A1, Lm2;
y = xx1 by A5, A3;
hence y = z by A5, A4; :: thesis: verum