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Metamath Proof Explorer

Theorem bnj226

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	bnj226.1	$⊢ B \subseteq C$
	Assertion	bnj226	$⊢ ⋃_{x \in A} B \subseteq C$

Step	Hyp	Ref	Expression
1		bnj226.1	$⊢ B \subseteq C$
2	1	rgenw	$⊢ \forall x \in A B \subseteq C$
3		iunss	$⊢ ⋃_{x \in A} B \subseteq C \leftrightarrow \forall x \in A B \subseteq C$
4	2 3	mpbir	$⊢ ⋃_{x \in A} B \subseteq C$