Theorem helloworld 27321

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	|- -. ( h e. ( L L 0 ) /\ W (/) ( R. 1 d ) )

Proof of Theorem helloworld

Step	Hyp	Ref	Expression
1		noel 3919	. . 3 |- -. <. W , ( R. 1 d ) >. e. (/)
2		df-br 4654	. . 3 |- ( W (/) ( R. 1 d ) <-> <. W , ( R. 1 d ) >. e. (/) )
3	1, 2	mtbir 313	. 2 |- -. W (/) ( R. 1 d )
4	3	intnan 960	1 |- -. ( h e. ( L L 0 ) /\ W (/) ( R. 1 d ) )

Syntax hints:   -. wn 3   /\ wa 384   e. wcel 1990   (/)c0 3915   <.cop 4183   class class class wbr 4653  (class class class)co 6650   R.cnr 9687   0cc0 9936   1c1 9937

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-dif 3577  df-nul 3916  df-br 4654

This theorem is referenced by: (None)