Metamath Proof Explorer

Theorem pm10.253

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

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

Proof

Step	Hyp	Ref	Expression
1		alex	⊢ ( ∀ 𝑥 𝜑 ↔ ¬ ∃ 𝑥 ¬ 𝜑 )
2	1	bicomi	⊢ ( ¬ ∃ 𝑥 ¬ 𝜑 ↔ ∀ 𝑥 𝜑 )
3	2	con1bii	⊢ ( ¬ ∀ 𝑥 𝜑 ↔ ∃ 𝑥 ¬ 𝜑 )