Theorem qexmid

Description: Quantified excluded middle (see exmid ). Also known as the drinker paradox (if ph ( x ) is interpreted as " x drinks", then this theorem tells that there exists a person such that, if this person drinks, then everyone drinks). Exercise 9.2a of Boolos, p. 111,Computability and Logic. (Contributed by NM, 10-Dec-2000)

	Ref	Expression
Assertion	qexmid	$$⊢\exists x\left(\phi \to \forall x\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		19.8a	$$⊢\forall x\phi \to \exists x\forall x\phi$$
2	1	19.35ri	$$⊢\exists x\left(\phi \to \forall x\phi \right)$$