Theorem bj-hbalt 37400

Description: Closed form of (general instance of) hbal 2204. (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 37399	1 ⊢ (∀𝑦(𝜑 → ∀𝑥𝜓) → (∀𝑦𝜑 → ∀𝑥∀𝑦𝜓))

This proof depends on syntax axioms:   → wi 4  ∀wal 1568

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1828  ax-4 1842  ax-11 2194

This theorem is used by:  bj-hbal  37401  bj-nfalt  37433  bj-cbv3ta  37516