let x1, y1, x2, x3 be set ; :: thesis: [:{x1,y1},{x2},{x3}:] = {[x1,x2,x3],[y1,x2,x3]}
thus [:{x1,y1},{x2},{x3}:] = [:[:{x1,y1},{x2}:],{x3}:] by ZFMISC_1:def 3
.= [:{[x1,x2],[y1,x2]},{x3}:] by ZFMISC_1:36
.= {[x1,x2,x3],[y1,x2,x3]} by ZFMISC_1:36 ; :: thesis: verum