let z, X1, X2, X3, X4, X5, X6 be set ; :: thesis: ( z in [:X1,X2,X3,X4,X5,X6:] implies ex x1, x2, x3, x4, x5, x6 being set st
( x1 in X1 & x2 in X2 & x3 in X3 & x4 in X4 & x5 in X5 & x6 in X6 & z = [x1,x2,x3,x4,x5,x6] ) )
assume z in [:X1,X2,X3,X4,X5,X6:] ; :: thesis: ex x1, x2, x3, x4, x5, x6 being set st
( x1 in X1 & x2 in X2 & x3 in X3 & x4 in X4 & x5 in X5 & x6 in X6 & z = [x1,x2,x3,x4,x5,x6] )
then consider x12345, x6 being set such that
A1: x12345 in [:X1,X2,X3,X4,X5:] and
A2: x6 in X6 and
A3: z = [x12345,x6] by ZFMISC_1:def 2;
consider x1, x2, x3, x4, x5 being set such that
A4: ( x1 in X1 & x2 in X2 & x3 in X3 & x4 in X4 & x5 in X5 ) and
A5: x12345 = [x1,x2,x3,x4,x5] by A1, Th30;
z = [x1,x2,x3,x4,x5,x6] by A3, A5;
hence ex x1, x2, x3, x4, x5, x6 being set st
( x1 in X1 & x2 in X2 & x3 in X3 & x4 in X4 & x5 in X5 & x6 in X6 & z = [x1,x2,x3,x4,x5,x6] ) by A2, A4; :: thesis: verum