Theorem helloworld 30497

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 4360	. . 3 ⊢ ¬ ⟨𝑊, (R1𝑑)⟩ ∈ ∅
2		df-br 5167	. . 3 ⊢ (𝑊∅(R1𝑑) ↔ ⟨𝑊, (R1𝑑)⟩ ∈ ∅)
3	1, 2	mtbir 323	. 2 ⊢ ¬ 𝑊∅(R1𝑑)
4	3	intnan 486	1 ⊢ ¬ (ℎ ∈ (𝐿𝐿0) ∧ 𝑊∅(R1𝑑))

Syntax hints:  ¬ wn 3   ∧ wa 395   ∈ wcel 2108  ∅c0 4352  ⟨cop 4654   class class class wbr 5166  (class class class)co 7448  Rcnr 10934  0cc0 11184  1c1 11185

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 2110  ax-9 2118  ax-ext 2711

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 2718  df-cleq 2732  df-clel 2819  df-dif 3979  df-nul 4353  df-br 5167

This theorem is referenced by: (None)