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Metamath Proof Explorer

Theorem bnj1361

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

		Ref	Expression
	Hypothesis	bnj1361.1	$⊢ φ \to \forall x (x \in A \to x \in B)$
	Assertion	bnj1361	$⊢ φ \to A \subseteq B$

Step	Hyp	Ref	Expression
1		bnj1361.1	$⊢ φ \to \forall x (x \in A \to x \in B)$
2		df-ss	$⊢ A \subseteq B \leftrightarrow \forall x (x \in A \to x \in B)$
3	1 2	sylibr	$⊢ φ \to A \subseteq B$