let A be partial non-empty UAStr ; LimDomRel A c= DomRel A
let x, y be object ; RELAT_1:def 3 ( not [x,y] in LimDomRel A or [x,y] in DomRel A )
assume A1:
[x,y] in LimDomRel A
; [x,y] in DomRel A
then A2:
x in the carrier of A
by ZFMISC_1:87;
y in the carrier of A
by A1, ZFMISC_1:87;
then
[x,y] in (DomRel A) |^ (A,0)
by A1, A2, Def7;
hence
[x,y] in DomRel A
by Th15; verum