Theorem bj-alexbiex 32690

Description: Adding a second quantifier is a tranparent operation, (∀∃ case). (Contributed by BJ, 20-Oct-2019.)

Assertion

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

Proof of Theorem bj-alexbiex

Step	Hyp	Ref	Expression
1		nfe1 2027	. 2 ⊢ Ⅎ𝑥∃𝑥𝜑
2	1	19.3 2069	1 ⊢ (∀𝑥∃𝑥𝜑 ↔ ∃𝑥𝜑)

Syntax hints:   ↔ wb 196  ∀wal 1481  ∃wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)