Theorem pm11.63

Description: Theorem *11.63 in WhiteheadRussell p. 166. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Assertion	pm11.63	$$⊢\neg \exists x\exists y\phi \to \forall x\forall y\left(\phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		2nexaln	$$⊢\neg \exists x\exists y\phi \leftrightarrow \forall x\forall y\neg \phi$$
2		pm2.21	$$⊢\neg \phi \to \left(\phi \to \psi \right)$$
3	2	2alimi	$$⊢\forall x\forall y\neg \phi \to \forall x\forall y\left(\phi \to \psi \right)$$
4	1 3	sylbi	$$⊢\neg \exists x\exists y\phi \to \forall x\forall y\left(\phi \to \psi \right)$$