Theorem qexmid 2063

Description: Quantified excluded middle (see exmid 431). 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.)

Assertion

Ref	Expression
qexmid	|- E. x ( ph -> A. x ph )

Proof of Theorem qexmid

Step	Hyp	Ref	Expression
1		19.8a 2052	. 2 |- ( A. x ph -> E. x A. x ph )
2	1	19.35ri 1807	1 |- E. x ( ph -> A. x ph )

Syntax hints:   -> wi 4   A.wal 1481   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by: (None)