Theorem bj-exexbiex 31878

Description: Adding a second quantifier is a tranparent 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 2014	. 2 ⊢ Ⅎ𝑥∃𝑥𝜑
2	1	19.9 2060	1 ⊢ (∃𝑥∃𝑥𝜑 ↔ ∃𝑥𝜑)

Syntax hints:   ↔ wb 195  ∃wex 1695

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nf 1701

This theorem is referenced by: (None)