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Theorem helloworld 28250
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 4247 . . 3 ¬ ⟨𝑊, (R1𝑑)⟩ ∈ ∅
2 df-br 5031 . . 3 (𝑊∅(R1𝑑) ↔ ⟨𝑊, (R1𝑑)⟩ ∈ ∅)
31, 2mtbir 326 . 2 ¬ 𝑊∅(R1𝑑)
43intnan 490 1 ¬ ( ∈ (𝐿𝐿0) ∧ 𝑊∅(R1𝑑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wa 399  wcel 2111  c0 4243  cop 4531   class class class wbr 5030  (class class class)co 7135  Rcnr 10276  0cc0 10526  1c1 10527
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-dif 3884  df-nul 4244  df-br 5031
This theorem is referenced by: (None)
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