Theorem bj-hbalt 37333

Description: Closed form of (general instance of) hbal 2201. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-hbalt	⊢ (∀𝑦(𝜑 → ∀𝑥𝜓) → (∀𝑦𝜑 → ∀𝑥∀𝑦𝜓))

Proof of Theorem bj-hbalt

Step	Hyp	Ref	Expression
1		id 23	. 2 ⊢ (∀𝑦(𝜑 → ∀𝑥𝜓) → ∀𝑦(𝜑 → ∀𝑥𝜓))
2		id 23	. 2 ⊢ ((𝜑 → ∀𝑥𝜓) → (𝜑 → ∀𝑥𝜓))
3	1, 2	bj-hbald 37332	1 ⊢ (∀𝑦(𝜑 → ∀𝑥𝜓) → (∀𝑦𝜑 → ∀𝑥∀𝑦𝜓))

This proof depends on syntax axioms:   → wi 4  ∀wal 1567

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1824  ax-4 1838  ax-11 2191

This theorem is used by:  bj-hbal  37334  bj-nfalt  37366  bj-cbv3ta  37449