let X1, X2, X3, X4, X5, Y1, Y2, Y3, Y4, Y5 be set ; :: thesis: ( [:X1,X2,X3,X4,X5:] meets [:Y1,Y2,Y3,Y4,Y5:] implies ( X1 meets Y1 & X2 meets Y2 & X3 meets Y3 & X4 meets Y4 & X5 meets Y5 ) )
assume A1: [:X1,X2,X3,X4,X5:] meets [:Y1,Y2,Y3,Y4,Y5:] ; :: thesis: ( X1 meets Y1 & X2 meets Y2 & X3 meets Y3 & X4 meets Y4 & X5 meets Y5 )
( [:[:[:[:X1,X2:],X3:],X4:],X5:] = [:X1,X2,X3,X4,X5:] & [:[:[:[:Y1,Y2:],Y3:],Y4:],Y5:] = [:Y1,Y2,Y3,Y4,Y5:] ) by Th9;
then A2: [:[:[:X1,X2:],X3:],X4:] meets [:[:[:Y1,Y2:],Y3:],Y4:] by A1, ZFMISC_1:104;
then A3: [:[:X1,X2:],X3:] meets [:[:Y1,Y2:],Y3:] by ZFMISC_1:104;
then [:X1,X2:] meets [:Y1,Y2:] by ZFMISC_1:104;
hence ( X1 meets Y1 & X2 meets Y2 & X3 meets Y3 & X4 meets Y4 & X5 meets Y5 ) by A1, A2, A3, ZFMISC_1:104; :: thesis: verum