Theorem bj-exalbial

Description: Adding a second quantifier over the same variable is a transparent operation, ( E. A. case). (Contributed by BJ, 20-Oct-2019)

	Ref	Expression
Assertion	bj-exalbial	⊢ ( ∃ 𝑥 ∀ 𝑥 𝜑 ↔ ∀ 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		nfa1	⊢ Ⅎ 𝑥 ∀ 𝑥 𝜑
2	1	19.9	⊢ ( ∃ 𝑥 ∀ 𝑥 𝜑 ↔ ∀ 𝑥 𝜑 )