Theorem alral

Description: Universal quantification implies restricted quantification. (Contributed by NM, 20-Oct-2006)

	Ref	Expression
Assertion	alral	$$⊢\forall x\phi \to \forall x\in A\phi$$

Proof

Step	Hyp	Ref	Expression
1		ala1	$$⊢\forall x\phi \to \forall x\left(x\in A\to \phi \right)$$
2		df-ral	$$⊢\forall x\in A\phi \leftrightarrow \forall x\left(x\in A\to \phi \right)$$
3	1 2	sylibr	$$⊢\forall x\phi \to \forall x\in A\phi$$