Theorem bnj1095

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

	Ref	Expression
Hypothesis	bnj1095.1	$$⊢\phi \leftrightarrow \forall x\in A\psi$$
Assertion	bnj1095	$$⊢\phi \to \forall x\phi$$

Proof

Step	Hyp	Ref	Expression
1		bnj1095.1	$$⊢\phi \leftrightarrow \forall x\in A\psi$$
2		hbra1	$$⊢\forall x\in A\psi \to \forall x\forall x\in A\psi$$
3	1 2	hbxfrbi	$$⊢\phi \to \forall x\phi$$