This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem fbelss

Description: An element of the filter base is a subset of the base set. (Contributed by Stefan O'Rear, 28-Jul-2015)

		Ref	Expression
	Assertion	fbelss	$⊢ (F \in fBas (B) \land X \in F) \to X \subseteq B$

Step	Hyp	Ref	Expression
1		fbsspw	$⊢ F \in fBas (B) \to F \subseteq 𝒫 B$
2	1	sselda	$⊢ (F \in fBas (B) \land X \in F) \to X \in 𝒫 B$
3	2	elpwid	$⊢ (F \in fBas (B) \land X \in F) \to X \subseteq B$