Theorem bj-bialal

Description: When ph is substituted for ps , both sides express a form of nonfreeness. (Contributed by BJ, 20-Oct-2019)

	Ref	Expression
Assertion	bj-bialal	⊢ ( ∀ 𝑥 ( ∀ 𝑥 𝜑 → 𝜓 ) ↔ ( ∀ 𝑥 𝜑 → ∀ 𝑥 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		nfa1	⊢ Ⅎ 𝑥 ∀ 𝑥 𝜑
2	1	19.21	⊢ ( ∀ 𝑥 ( ∀ 𝑥 𝜑 → 𝜓 ) ↔ ( ∀ 𝑥 𝜑 → ∀ 𝑥 𝜓 ) )