Theorem ralrid

Description: Sufficient condition for the restricted universal quantifier. Deduction form. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

	Ref	Expression
Hypothesis	ralrid.1	$$⊢\phi \to \forall x\left(x\in A\to \psi \right)$$
Assertion	ralrid	$$⊢\phi \to \forall x\in A\psi$$

Proof

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