let X1, X2, X3, X4, X5, X6, Y1, Y2, Y3, Y4, Y5, Y6 be set ; :: thesis: ( X1 c= Y1 & X2 c= Y2 & X3 c= Y3 & X4 c= Y4 & X5 c= Y5 & X6 c= Y6 implies [:X1,X2,X3,X4,X5,X6:] c= [:Y1,Y2,Y3,Y4,Y5,Y6:] )
assume ( X1 c= Y1 & X2 c= Y2 & X3 c= Y3 & X4 c= Y4 & X5 c= Y5 ) ; :: thesis: ( not X6 c= Y6 or [:X1,X2,X3,X4,X5,X6:] c= [:Y1,Y2,Y3,Y4,Y5,Y6:] )
then A1: [:X1,X2,X3,X4,X5:] c= [:Y1,Y2,Y3,Y4,Y5:] by Th35;
assume X6 c= Y6 ; :: thesis: [:X1,X2,X3,X4,X5,X6:] c= [:Y1,Y2,Y3,Y4,Y5,Y6:]
hence [:X1,X2,X3,X4,X5,X6:] c= [:Y1,Y2,Y3,Y4,Y5,Y6:] by A1, ZFMISC_1:119; :: thesis: verum