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Mirrors > Home > MPE Home > Th. List > qexmid | Structured version Visualization version GIF version |
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) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.8a 2039 | . 2 ⊢ (∀𝑥𝜑 → ∃𝑥∀𝑥𝜑) | |
2 | 1 | 19.35ri 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) |
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