let A, B, C, p be set ; ( A /\ C = {p} & p in B & B c= C implies A /\ B = {p} )
assume that
A1:
A /\ C = {p}
and
A2:
p in B
and
A3:
B c= C
; A /\ B = {p}
A4:
{p} c= B
by A2, Lm1;
thus A /\ B =
A /\ (C /\ B)
by A3, XBOOLE_1:28
.=
{p} /\ B
by A1, XBOOLE_1:16
.=
{p}
by A4, XBOOLE_1:28
; verum