Theorem bnj1142

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

	Ref	Expression
Hypothesis	bnj1142.1	$$⊢\phi \to \forall x\left(x\in A\to \psi \right)$$
Assertion	bnj1142	$$⊢\phi \to \forall x\in A\psi$$

Proof

Step	Hyp	Ref	Expression
1		bnj1142.1	$$⊢\phi \to \forall x\left(x\in A\to \psi \right)$$
2		df-ral	$$⊢\forall x\in A\psi \leftrightarrow \forall x\left(x\in A\to \psi \right)$$
3	1 2	sylibr	$$⊢\phi \to \forall x\in A\psi$$