Theorem pm10.252

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

	Ref	Expression
Assertion	pm10.252	$$⊢\neg \exists x\phi \leftrightarrow \forall x\neg \phi$$

Proof

Step	Hyp	Ref	Expression
1		df-ex	$$⊢\exists x\phi \leftrightarrow \neg \forall x\neg \phi$$
2	1	bicomi	$$⊢\neg \forall x\neg \phi \leftrightarrow \exists x\phi$$
3	2	con1bii	$$⊢\neg \exists x\phi \leftrightarrow \forall x\neg \phi$$