Theorem bj-exexbiex 37353

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

Assertion

Ref	Expression
bj-exexbiex	⊢ (∃𝑥∃𝑥𝜑 ↔ ∃𝑥𝜑)

Proof of Theorem bj-exexbiex

Step	Hyp	Ref	Expression
1		nfe1 2184	. 2 ⊢ Ⅎ𝑥∃𝑥𝜑
2	1	19.9 2240	1 ⊢ (∃𝑥∃𝑥𝜑 ↔ ∃𝑥𝜑)

This proof depends on syntax axioms:   ↔ wb 209  ∃wex 1808

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-10 2175  ax-12 2212

This proof depends on definitions:  df-bi 210  df-ex 1809  df-nf 1813

This theorem is used by: (None)