Theorem pm10.253 40700

Description: Theorem *10.253 in [WhiteheadRussell] p. 149. (Contributed by Andrew Salmon, 17-Jun-2011.)

Assertion

Ref	Expression
pm10.253	⊢ (¬ ∀𝑥𝜑 ↔ ∃𝑥 ¬ 𝜑)

Proof of Theorem pm10.253

Step	Hyp	Ref	Expression
1		alex 1825	. . 3 ⊢ (∀𝑥𝜑 ↔ ¬ ∃𝑥 ¬ 𝜑)
2	1	bicomi 226	. 2 ⊢ (¬ ∃𝑥 ¬ 𝜑 ↔ ∀𝑥𝜑)
3	2	con1bii 359	1 ⊢ (¬ ∀𝑥𝜑 ↔ ∃𝑥 ¬ 𝜑)

Syntax hints:  ¬ wn 3   ↔ wb 208  ∀wal 1534  ∃wex 1779

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809

This theorem depends on definitions:  df-bi 209  df-ex 1780

This theorem is referenced by: (None)