Theorem pm10.252 44380

Description: Theorem *10.252 in [WhiteheadRussell] p. 149. (Contributed by Andrew Salmon, 17-Jun-2011.) (New usage is discouraged.)

Assertion

Ref	Expression
pm10.252	⊢ (¬ ∃𝑥𝜑 ↔ ∀𝑥 ¬ 𝜑)

Proof of Theorem pm10.252

Step	Hyp	Ref	Expression
1		df-ex 1780	. . 3 ⊢ (∃𝑥𝜑 ↔ ¬ ∀𝑥 ¬ 𝜑)
2	1	bicomi 224	. 2 ⊢ (¬ ∀𝑥 ¬ 𝜑 ↔ ∃𝑥𝜑)
3	2	con1bii 356	1 ⊢ (¬ ∃𝑥𝜑 ↔ ∀𝑥 ¬ 𝜑)

Syntax hints:  ¬ wn 3   ↔ wb 206  ∀wal 1538  ∃wex 1779

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-ex 1780

This theorem is referenced by: (None)