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Theorem helloworld 30488
Description: The classic "Hello world" benchmark has been translated into 314 computer programming languages - see http://helloworldcollection.de. 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 to put it to rest with a remarkably short proof only four 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 4355 . . 3 ¬ ⟨𝑊, (R1𝑑)⟩ ∈ ∅
2 df-br 5170 . . 3 (𝑊∅(R1𝑑) ↔ ⟨𝑊, (R1𝑑)⟩ ∈ ∅)
31, 2mtbir 323 . 2 ¬ 𝑊∅(R1𝑑)
43intnan 486 1 ¬ ( ∈ (𝐿𝐿0) ∧ 𝑊∅(R1𝑑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wa 395  wcel 2103  c0 4347  cop 4654   class class class wbr 5169  (class class class)co 7445  Rcnr 10930  0cc0 11180  1c1 11181
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2105  ax-9 2113  ax-ext 2705
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2712  df-cleq 2726  df-clel 2813  df-dif 3973  df-nul 4348  df-br 5170
This theorem is referenced by: (None)
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