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 ↔ ∀ 𝑥 ∈ 𝐴 𝜓 )
Assertion	bnj1095	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		bnj1095.1	⊢ ( 𝜑 ↔ ∀ 𝑥 ∈ 𝐴 𝜓 )
2		hbra1	⊢ ( ∀ 𝑥 ∈ 𝐴 𝜓 → ∀ 𝑥 ∀ 𝑥 ∈ 𝐴 𝜓 )
3	1 2	hbxfrbi	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )