Theorem bj-hbalt

Description: Closed form of (general instance of) hbal . (Contributed by BJ, 2-May-2019)

	Ref	Expression
Assertion	bj-hbalt	⊢ ( ∀ 𝑦 ( 𝜑 → ∀ 𝑥 𝜓 ) → ( ∀ 𝑦 𝜑 → ∀ 𝑥 ∀ 𝑦 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( ∀ 𝑦 ( 𝜑 → ∀ 𝑥 𝜓 ) → ∀ 𝑦 ( 𝜑 → ∀ 𝑥 𝜓 ) )
2		id	⊢ ( ( 𝜑 → ∀ 𝑥 𝜓 ) → ( 𝜑 → ∀ 𝑥 𝜓 ) )
3	1 2	bj-hbald	⊢ ( ∀ 𝑦 ( 𝜑 → ∀ 𝑥 𝜓 ) → ( ∀ 𝑦 𝜑 → ∀ 𝑥 ∀ 𝑦 𝜓 ) )