Theorem bnj946

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

	Ref	Expression
Hypothesis	bnj946.1	$$⊢\phi \leftrightarrow \forall x\in A\psi$$
Assertion	bnj946	$$⊢\phi \leftrightarrow \forall x\left(x\in A\to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bnj946.1	$$⊢\phi \leftrightarrow \forall x\in A\psi$$
2		df-ral	$$⊢\forall x\in A\psi \leftrightarrow \forall x\left(x\in A\to \psi \right)$$
3	1 2	bitri	$$⊢\phi \leftrightarrow \forall x\left(x\in A\to \psi \right)$$