let A be 1 -element set ; for B being set st not A /\ B is empty holds
A c= B
let B be set ; ( not A /\ B is empty implies A c= B )
A1:
A /\ B c= B
by XBOOLE_1:17;
assume
not A /\ B is empty
; A c= B
then consider a being object such that
A2:
a in A /\ B
;
A3:
ex s being Element of A st A = {s}
by SUBSET_1:46;
A /\ B c= A
by XBOOLE_1:17;
then
{a} c= A
by A2, ZFMISC_1:31;
then
{a} = A
by A3, ZFMISC_1:18;
hence
A c= B
by A2, A1, ZFMISC_1:31; verum