Theorem pm10.251 40712

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

Step	Hyp	Ref	Expression
1		alnex 1782	. 2 ⊢ (∀𝑥 ¬ 𝜑 ↔ ¬ ∃𝑥𝜑)
2		19.2 1981	. . 3 ⊢ (∀𝑥𝜑 → ∃𝑥𝜑)
3	2	con3i 157	. 2 ⊢ (¬ ∃𝑥𝜑 → ¬ ∀𝑥𝜑)
4	1, 3	sylbi 219	1 ⊢ (∀𝑥 ¬ 𝜑 → ¬ ∀𝑥𝜑)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1535  ∃wex 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-6 1970

This theorem depends on definitions:  df-bi 209  df-ex 1781

This theorem is referenced by: (None)