Users' Mathboxes Mathbox for Andrew Salmon < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  pm10.253 Structured version   Visualization version   GIF version

Theorem pm10.253 38878
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 1793 . . 3 (∀𝑥𝜑 ↔ ¬ ∃𝑥 ¬ 𝜑)
21bicomi 214 . 2 (¬ ∃𝑥 ¬ 𝜑 ↔ ∀𝑥𝜑)
32con1bii 345 1 (¬ ∀𝑥𝜑 ↔ ∃𝑥 ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wal 1521  wex 1744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777
This theorem depends on definitions:  df-bi 197  df-ex 1745
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator