let X1, X2, X3, Y1, Y2, Y3 be set ; :: thesis: ( X1 c= Y1 & X2 c= Y2 & X3 c= Y3 implies [:X1,X2,X3:] c= [:Y1,Y2,Y3:] )
A1: ( [:X1,X2,X3:] = [:[:X1,X2:],X3:] & [:Y1,Y2,Y3:] = [:[:Y1,Y2:],Y3:] ) by ZFMISC_1:def 3;
assume ( X1 c= Y1 & X2 c= Y2 ) ; :: thesis: ( not X3 c= Y3 or [:X1,X2,X3:] c= [:Y1,Y2,Y3:] )
then A2: [:X1,X2:] c= [:Y1,Y2:] by ZFMISC_1:96;
assume X3 c= Y3 ; :: thesis: [:X1,X2,X3:] c= [:Y1,Y2,Y3:]
hence [:X1,X2,X3:] c= [:Y1,Y2,Y3:] by A2, A1, ZFMISC_1:96; :: thesis: verum