let X1, Y1, X2, Y2, X3, Y3, X4, Y4 be set ; :: thesis: ( X1 c= Y1 & X2 c= Y2 & X3 c= Y3 & X4 c= Y4 implies [:X1,X2,X3,X4:] c= [:Y1,Y2,Y3,Y4:] )
assume ( X1 c= Y1 & X2 c= Y2 & X3 c= Y3 ) ; :: thesis: ( not X4 c= Y4 or [:X1,X2,X3,X4:] c= [:Y1,Y2,Y3,Y4:] )
then A1: [:X1,X2,X3:] c= [:Y1,Y2,Y3:] by Th77;
A2: ( [:X1,X2,X3,X4:] = [:[:X1,X2,X3:],X4:] & [:Y1,Y2,Y3,Y4:] = [:[:Y1,Y2,Y3:],Y4:] ) by ZFMISC_1:def 4;
assume X4 c= Y4 ; :: thesis: [:X1,X2,X3,X4:] c= [:Y1,Y2,Y3,Y4:]
hence [:X1,X2,X3,X4:] c= [:Y1,Y2,Y3,Y4:] by A1, A2, ZFMISC_1:119; :: thesis: verum