Theorem pm10.53

Description: Theorem *10.53 in WhiteheadRussell p. 155. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Assertion	pm10.53	$$⊢\neg \exists x\phi \to \forall x\left(\phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		pm2.21	$$⊢\neg \exists x\phi \to \left(\exists x\phi \to \forall x\psi \right)$$
2		19.38	$$⊢\left(\exists x\phi \to \forall x\psi \right)\to \forall x\left(\phi \to \psi \right)$$
3	1 2	syl	$$⊢\neg \exists x\phi \to \forall x\left(\phi \to \psi \right)$$