Theorem bj-exexbiex

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

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

Proof

Step	Hyp	Ref	Expression
1		nfe1	⊢ Ⅎ 𝑥 ∃ 𝑥 𝜑
2	1	19.9	⊢ ( ∃ 𝑥 ∃ 𝑥 𝜑 ↔ ∃ 𝑥 𝜑 )