let L be non empty RelStr ; :: thesis: for x being set holds
( x is Element of (Subalgebras L) iff x is strict closure directed-sups-inheriting System of L )
let x be set ; :: thesis: ( x is Element of (Subalgebras L) iff x is strict closure directed-sups-inheriting System of L )
( x is Element of (ClosureSystems L) iff x is strict closure System of L ) by Th17;
hence ( x is Element of (Subalgebras L) iff x is strict closure directed-sups-inheriting System of L ) by Def8, YELLOW_0:58; :: thesis: verum