Theorem 2exnexn

Description: Theorem *11.51 in WhiteheadRussell p. 164. (Contributed by Andrew Salmon, 24-May-2011) (Proof shortened by Wolf Lammen, 25-Sep-2014)

	Ref	Expression
Assertion	2exnexn	⊢ ( ∃ 𝑥 ∀ 𝑦 𝜑 ↔ ¬ ∀ 𝑥 ∃ 𝑦 ¬ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		alexn	⊢ ( ∀ 𝑥 ∃ 𝑦 ¬ 𝜑 ↔ ¬ ∃ 𝑥 ∀ 𝑦 𝜑 )
2	1	con2bii	⊢ ( ∃ 𝑥 ∀ 𝑦 𝜑 ↔ ¬ ∀ 𝑥 ∃ 𝑦 ¬ 𝜑 )