let x1, y1, x2, x3, y3 be set ; :: thesis: [:{x1,y1},{x2},{x3,y3}:] = {[x1,x2,x3],[y1,x2,x3],[x1,x2,y3],[y1,x2,y3]}
thus [:{x1,y1},{x2},{x3,y3}:] = [:[:{x1,y1},{x2}:],{x3,y3}:] by ZFMISC_1:def 3
.= [:{[x1,x2],[y1,x2]},{x3,y3}:] by ZFMISC_1:30
.= {[[x1,x2],x3],[[x1,x2],y3],[[y1,x2],x3],[[y1,x2],y3]} by Th25
.= {[x1,x2,x3],[y1,x2,x3],[x1,x2,y3],[y1,x2,y3]} by ENUMSET1:62 ; :: thesis: verum