Theorem pm10.251 45128

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 1814	. 2 ⊢ (∀𝑥 ¬ 𝜑 ↔ ¬ ∃𝑥𝜑)
2		19.2 2009	. . 3 ⊢ (∀𝑥𝜑 → ∃𝑥𝜑)
3	2	con3i 155	. 2 ⊢ (¬ ∃𝑥𝜑 → ¬ ∀𝑥𝜑)
4	1, 3	sylbi 220	1 ⊢ (∀𝑥 ¬ 𝜑 → ¬ ∀𝑥𝜑)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4  ∀wal 1568  ∃wex 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-6 2000

This proof depends on definitions:  df-bi 210  df-ex 1813

This theorem is used by: (None)