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Theorem bj-exexbiex 32666
Description: Adding a second quantifier is a tranparent operation, (∃∃ case). (Contributed by BJ, 20-Oct-2019.)
Assertion
Ref Expression
bj-exexbiex (∃𝑥𝑥𝜑 ↔ ∃𝑥𝜑)

Proof of Theorem bj-exexbiex
StepHypRef Expression
1 nfe1 2025 . 2 𝑥𝑥𝜑
2119.9 2070 1 (∃𝑥𝑥𝜑 ↔ ∃𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wex 1702
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-10 2017  ax-12 2045
This theorem depends on definitions:  df-bi 197  df-ex 1703  df-nf 1708
This theorem is referenced by: (None)
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