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Theorem 2nexaln 1831
Description: Theorem *11.25 in [WhiteheadRussell] p. 160. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
2nexaln (¬ ∃𝑥𝑦𝜑 ↔ ∀𝑥𝑦 ¬ 𝜑)

Proof of Theorem 2nexaln
StepHypRef Expression
1 2exnaln 1830 . . 3 (∃𝑥𝑦𝜑 ↔ ¬ ∀𝑥𝑦 ¬ 𝜑)
21bicomi 227 . 2 (¬ ∀𝑥𝑦 ¬ 𝜑 ↔ ∃𝑥𝑦𝜑)
32con1bii 360 1 (¬ ∃𝑥𝑦𝜑 ↔ ∀𝑥𝑦 ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 209  wal 1536  wex 1781
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811
This theorem depends on definitions:  df-bi 210  df-ex 1782
This theorem is referenced by:  cbvex2  2436  2mo  2736  bj-alcomexcom  34071  pm11.63  41019  fun2dmnopgexmpl  43766  spr0nelg  43919
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