let X0 be non empty SubSpace of X; :: thesis: X0 is V144()

reconsider A0 = the carrier of X0 as non empty Subset of X by TSEP_1:1;

X is SubSpace of X by TSEP_1:2;

then reconsider A = the carrier of X as non empty Subset of X by TSEP_1:1;

A is T_0 by Th4;

then A0 is T_0 ;

hence X0 is V144() ; :: thesis: verum

reconsider A0 = the carrier of X0 as non empty Subset of X by TSEP_1:1;

X is SubSpace of X by TSEP_1:2;

then reconsider A = the carrier of X as non empty Subset of X by TSEP_1:1;

A is T_0 by Th4;

then A0 is T_0 ;

hence X0 is V144() ; :: thesis: verum