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