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Theorem bj-exalbial 36088
Description: Adding a second quantifier over the same variable is a transparent operation, (∃∀ case). (Contributed by BJ, 20-Oct-2019.)
Assertion
Ref Expression
bj-exalbial (∃𝑥𝑥𝜑 ↔ ∀𝑥𝜑)

Proof of Theorem bj-exalbial
StepHypRef Expression
1 nfa1 2140 . 2 𝑥𝑥𝜑
2119.9 2190 1 (∃𝑥𝑥𝜑 ↔ ∀𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 205  wal 1531  wex 1773
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-10 2129  ax-12 2163
This theorem depends on definitions:  df-bi 206  df-or 845  df-ex 1774  df-nf 1778
This theorem is referenced by: (None)
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