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Theorem bj-exalbial 33030
Description: Adding a second quantifier is a tranparent operation, (∃∀ case). (Contributed by BJ, 20-Oct-2019.)
Assertion
Ref Expression
bj-exalbial (∃𝑥𝑥𝜑 ↔ ∀𝑥𝜑)

Proof of Theorem bj-exalbial
StepHypRef Expression
1 nfa1 2184 . 2 𝑥𝑥𝜑
2119.9 2228 1 (∃𝑥𝑥𝜑 ↔ ∀𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wal 1629  wex 1852
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-10 2174  ax-12 2203
This theorem depends on definitions:  df-bi 197  df-or 837  df-ex 1853  df-nf 1858
This theorem is referenced by: (None)
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