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Theorem 2nexaln 1930
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 1929 . . 3 (∃𝑥𝑦𝜑 ↔ ¬ ∀𝑥𝑦 ¬ 𝜑)
21bicomi 216 . 2 (¬ ∀𝑥𝑦 ¬ 𝜑 ↔ ∃𝑥𝑦𝜑)
32con1bii 348 1 (¬ ∃𝑥𝑦𝜑 ↔ ∀𝑥𝑦 ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 198  wal 1656  wex 1880
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910
This theorem depends on definitions:  df-bi 199  df-ex 1881
This theorem is referenced by:  cbvex2  2431  2mo  2731  bj-alcomexcom  33205  pm11.63  39435  fun2dmnopgexmpl  42187  spr0nelg  42573
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