Theorem bj-alexbiex

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

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

Proof

Step	Hyp	Ref	Expression
1		nfe1	⊢ Ⅎ 𝑥 ∃ 𝑥 𝜑
2	1	19.3	⊢ ( ∀ 𝑥 ∃ 𝑥 𝜑 ↔ ∃ 𝑥 𝜑 )