Theorem bj-hbal 37334

Description: More general instance of hbal 2201. (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 37333	. 2 ⊢ (∀𝑦(𝜑 → ∀𝑥𝜓) → (∀𝑦𝜑 → ∀𝑥∀𝑦𝜓))
2		bj-hbal.1	. 2 ⊢ (𝜑 → ∀𝑥𝜓)
3	1, 2	mpg 1826	1 ⊢ (∀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: (None)