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Theorem pm10.251 37384
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 1696 . 2 (∀𝑥 ¬ 𝜑 ↔ ¬ ∃𝑥𝜑)
2 19.2 1878 . . 3 (∀𝑥𝜑 → ∃𝑥𝜑)
32con3i 148 . 2 (¬ ∃𝑥𝜑 → ¬ ∀𝑥𝜑)
41, 3sylbi 205 1 (∀𝑥 ¬ 𝜑 → ¬ ∀𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1472  wex 1694
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-6 1874
This theorem depends on definitions:  df-bi 195  df-ex 1695
This theorem is referenced by: (None)
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