Theorem bnj1211

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

	Ref	Expression
Hypothesis	bnj1211.1	$$⊢\phi \to \forall x\in A\psi$$
Assertion	bnj1211	$$⊢\phi \to \forall x\left(x\in A\to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bnj1211.1	$$⊢\phi \to \forall x\in A\psi$$
2		df-ral	$$⊢\forall x\in A\psi \leftrightarrow \forall x\left(x\in A\to \psi \right)$$
3	1 2	sylib	$$⊢\phi \to \forall x\left(x\in A\to \psi \right)$$