Theorem bj-hbal 36946

Description: More general instance of hbal 2173. (Contributed by BJ, 4-Apr-2026.)

Hypothesis

Ref	Expression
bj-hbal.1	⊢ (𝜑 → ∀𝑥𝜓)

Assertion

Ref	Expression
bj-hbal	⊢ (∀𝑦𝜑 → ∀𝑥∀𝑦𝜓)

Proof of Theorem bj-hbal

Step	Hyp	Ref	Expression
1		bj-hbalt 36945	. 2 ⊢ (∀𝑦(𝜑 → ∀𝑥𝜓) → (∀𝑦𝜑 → ∀𝑥∀𝑦𝜓))
2		bj-hbal.1	. 2 ⊢ (𝜑 → ∀𝑥𝜓)
3	1, 2	mpg 1799	1 ⊢ (∀𝑦𝜑 → ∀𝑥∀𝑦𝜓)

Syntax hints:   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1797  ax-4 1811  ax-11 2163

This theorem is referenced by: (None)