Theorem bj-hbalt 37036

Description: Closed form of (general instance of) hbal 2180. (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 22	. 2 ⊢ (∀𝑦(𝜑 → ∀𝑥𝜓) → ∀𝑦(𝜑 → ∀𝑥𝜓))
2		id 22	. 2 ⊢ ((𝜑 → ∀𝑥𝜓) → (𝜑 → ∀𝑥𝜓))
3	1, 2	bj-hbald 37035	1 ⊢ (∀𝑦(𝜑 → ∀𝑥𝜓) → (∀𝑦𝜑 → ∀𝑥∀𝑦𝜓))

Syntax hints:   → wi 4  ∀wal 1546

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1803  ax-4 1817  ax-11 2170

This theorem is referenced by:  bj-hbal  37037  bj-nfalt  37069  bj-cbv3ta  37152