let x1, x2, x3, x4, X1, X2, X3, X4 be set ; :: thesis: ( [x1,x2,x3,x4] in [:X1,X2,X3,X4:] iff ( x1 in X1 & x2 in X2 & x3 in X3 & x4 in X4 ) )
A1: [:X1,X2,X3,X4:] = [:[:X1,X2:],X3,X4:] by Th54;
A2: [x1,x2,x3,x4] = [[x1,x2],x3,x4] ;
( [x1,x2] in [:X1,X2:] iff ( x1 in X1 & x2 in X2 ) ) by ZFMISC_1:106;
hence ( [x1,x2,x3,x4] in [:X1,X2,X3,X4:] iff ( x1 in X1 & x2 in X2 & x3 in X3 & x4 in X4 ) ) by A1, A2, Th73; :: thesis: verum