Theorem ntrss3

Description: The interior of a subset of a topological space is included in the space. (Contributed by NM, 1-Oct-2007)

	Ref	Expression
Hypothesis	clscld.1	|- X = U. J
Assertion	ntrss3	|- ( ( J e. Top /\ S C_ X ) -> ( ( int ` J ) ` S ) C_ X )

Proof

Step	Hyp	Ref	Expression
1		clscld.1	|- X = U. J
2	1	ntropn	|- ( ( J e. Top /\ S C_ X ) -> ( ( int ` J ) ` S ) e. J )
3	1	eltopss	|- ( ( J e. Top /\ ( ( int ` J ) ` S ) e. J ) -> ( ( int ` J ) ` S ) C_ X )
4	2 3	syldan	|- ( ( J e. Top /\ S C_ X ) -> ( ( int ` J ) ` S ) C_ X )