Theorem helloworld 28829

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	⊢ ¬ (ℎ ∈ (𝐿𝐿0) ∧ 𝑊∅(R1𝑑))

Proof of Theorem helloworld

Step	Hyp	Ref	Expression
1		noel 4264	. . 3 ⊢ ¬ ⟨𝑊, (R1𝑑)⟩ ∈ ∅
2		df-br 5075	. . 3 ⊢ (𝑊∅(R1𝑑) ↔ ⟨𝑊, (R1𝑑)⟩ ∈ ∅)
3	1, 2	mtbir 323	. 2 ⊢ ¬ 𝑊∅(R1𝑑)
4	3	intnan 487	1 ⊢ ¬ (ℎ ∈ (𝐿𝐿0) ∧ 𝑊∅(R1𝑑))

Syntax hints:  ¬ wn 3   ∧ wa 396   ∈ wcel 2106  ∅c0 4256  ⟨cop 4567   class class class wbr 5074  (class class class)co 7275  Rcnr 10621  0cc0 10871  1c1 10872

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-fal 1552  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-dif 3890  df-nul 4257  df-br 5075

This theorem is referenced by: (None)