MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  qexmid Structured version   Visualization version   GIF version

Theorem qexmid 2051
Description: Quantified excluded middle (see exmid 430). Also known as the drinker paradox (if 𝜑(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
qexmid 𝑥(𝜑 → ∀𝑥𝜑)

Proof of Theorem qexmid
StepHypRef Expression
1 19.8a 2039 . 2 (∀𝑥𝜑 → ∃𝑥𝑥𝜑)
2119.35ri 1796 1 𝑥(𝜑 → ∀𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1473  wex 1695
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034
This theorem depends on definitions:  df-bi 196  df-ex 1696
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator