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Theorem pm10.253 39101
Description: Theorem *10.253 in [WhiteheadRussell] p. 149. (Contributed by Andrew Salmon, 17-Jun-2011.)
Assertion
Ref Expression
pm10.253 (¬ ∀𝑥𝜑 ↔ ∃𝑥 ¬ 𝜑)

Proof of Theorem pm10.253
StepHypRef Expression
1 alex 1904 . . 3 (∀𝑥𝜑 ↔ ¬ ∃𝑥 ¬ 𝜑)
21bicomi 215 . 2 (¬ ∃𝑥 ¬ 𝜑 ↔ ∀𝑥𝜑)
32con1bii 346 1 (¬ ∀𝑥𝜑 ↔ ∃𝑥 ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 197  wal 1632  wex 1855
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1873  ax-4 1888
This theorem depends on definitions:  df-bi 198  df-ex 1856
This theorem is referenced by: (None)
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