Users' Mathboxes Mathbox for Andrew Salmon < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  pm10.251 Structured version   Visualization version   GIF version

Theorem pm10.251 39078
Description: Theorem *10.251 in [WhiteheadRussell] p. 149. (Contributed by Andrew Salmon, 17-Jun-2011.)
Assertion
Ref Expression
pm10.251 (∀𝑥 ¬ 𝜑 → ¬ ∀𝑥𝜑)

Proof of Theorem pm10.251
StepHypRef Expression
1 alnex 1853 . 2 (∀𝑥 ¬ 𝜑 ↔ ¬ ∃𝑥𝜑)
2 19.2 2060 . . 3 (∀𝑥𝜑 → ∃𝑥𝜑)
32con3i 151 . 2 (¬ ∃𝑥𝜑 → ¬ ∀𝑥𝜑)
41, 3sylbi 207 1 (∀𝑥 ¬ 𝜑 → ¬ ∀𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1628  wex 1851
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-6 2056
This theorem depends on definitions:  df-bi 197  df-ex 1852
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator