This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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	$⊢ φ \leftrightarrow \forall x \in A ψ$
	Assertion	bnj1095	$⊢ φ \to \forall x φ$

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