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Theorem helloworld 27451
Description: The classic "Hello world" benchmark has been translated into 314 computer programming languages - see http://www.roesler-ac.de/wolfram/hello.htm. However, for many years it eluded a proof that it is more than just a conjecture, even though a wily mathematician once claimed, "I have discovered a truly marvelous proof of this, which this margin is too narrow to contain." Using an IBM 709 mainframe, a team of mathematicians led by Prof. Loof Lirpa, at the New College of Tahiti, were finally able put it rest with a remarkably short proof only 4 lines long. (Contributed by Prof. Loof Lirpa, 1-Apr-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
helloworld ¬ ( ∈ (𝐿𝐿0) ∧ 𝑊∅(R1𝑑))

Proof of Theorem helloworld
StepHypRef Expression
1 noel 3952 . . 3 ¬ ⟨𝑊, (R1𝑑)⟩ ∈ ∅
2 df-br 4686 . . 3 (𝑊∅(R1𝑑) ↔ ⟨𝑊, (R1𝑑)⟩ ∈ ∅)
31, 2mtbir 312 . 2 ¬ 𝑊∅(R1𝑑)
43intnan 980 1 ¬ ( ∈ (𝐿𝐿0) ∧ 𝑊∅(R1𝑑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wa 383  wcel 2030  c0 3948  cop 4216   class class class wbr 4685  (class class class)co 6690  Rcnr 9725  0cc0 9974  1c1 9975
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-v 3233  df-dif 3610  df-nul 3949  df-br 4686
This theorem is referenced by: (None)
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