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Metamath Proof Explorer

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	\|- E. x ( ph -> A. x ph )

Proof

Step	Hyp	Ref	Expression
1		19.8a	\|- ( A. x ph -> E. x A. x ph )
2	1	19.35ri	\|- E. x ( ph -> A. x ph )