let x1, x2, x3, y1, y2 be object ; :: thesis: [:{x1,y1},{x2,y2},{x3}:] = {[x1,x2,x3],[y1,x2,x3],[x1,y2,x3],[y1,y2,x3]}
thus [:{x1,y1},{x2,y2},{x3}:] = [:[:{x1,y1},{x2,y2}:],{x3}:] by ZFMISC_1:def 3
.= [:{[x1,x2],[x1,y2],[y1,x2],[y1,y2]},{x3}:] by Th17
.= [:({[x1,x2],[x1,y2]} \/ {[y1,x2],[y1,y2]}),{x3}:] by ENUMSET1:5
.= [:{[x1,x2],[x1,y2]},{x3}:] \/ [:{[y1,x2],[y1,y2]},{x3}:] by ZFMISC_1:97
.= {[[x1,x2],x3],[[x1,y2],x3]} \/ [:{[y1,x2],[y1,y2]},{x3}:] by ZFMISC_1:30
.= {[[x1,x2],x3],[[x1,y2],x3]} \/ {[[y1,x2],x3],[[y1,y2],x3]} by ZFMISC_1:30
.= {[x1,x2,x3],[x1,y2,x3],[y1,x2,x3],[[y1,y2],x3]} by ENUMSET1:5
.= {[x1,x2,x3],[y1,x2,x3],[x1,y2,x3],[y1,y2,x3]} by ENUMSET1:62 ; :: thesis: verum