let X1, X2, X3, X4, Y1, Y2, Y3, 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:] )
A1: ( [:X1,X2,X3,X4:] = [:[:X1,X2,X3:],X4:] & [:Y1,Y2,Y3,Y4:] = [:[:Y1,Y2,Y3:],Y4:] ) by ZFMISC_1:def 4;
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 A2: [:X1,X2,X3:] c= [:Y1,Y2,Y3:] by Th58;
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 A2, A1, ZFMISC_1:96; :: thesis: verum