let x1, x2, x3 be object ; :: thesis: for X1, X2, X3 being set holds
( [x1,x2,x3] in [:X1,X2,X3:] iff ( x1 in X1 & x2 in X2 & x3 in X3 ) )
let X1, X2, X3 be set ; :: thesis: ( [x1,x2,x3] in [:X1,X2,X3:] iff ( x1 in X1 & x2 in X2 & x3 in X3 ) )
A1: ( [x1,x2] in [:X1,X2:] iff ( x1 in X1 & x2 in X2 ) ) by ZFMISC_1:87;
[:X1,X2,X3:] = [:[:X1,X2:],X3:] by ZFMISC_1:def 3;
hence ( [x1,x2,x3] in [:X1,X2,X3:] iff ( x1 in X1 & x2 in X2 & x3 in X3 ) ) by A1, ZFMISC_1:87; :: thesis: verum