Metamath Proof Explorer


Theorem 9p10ne21fool

Description: 9 + 10 equals 21. This astonishing thesis lives as a meme on the internet, and may be believed by quite some people. At least repeated requests to falsify it are a permanent part of the story. Prof. Loof Lirpa did not rest until he finally came up with a computer verifiable mathematical proof, that only a fool can think so. (Contributed by Prof. Loof Lirpa, 26-Aug-2023) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion 9p10ne21fool
|- ( ( 9 + ; 1 0 ) = ; 2 1 -> F (/) ( 0 x. 1 ) )

Proof

Step Hyp Ref Expression
1 9p10ne21
 |-  ( 9 + ; 1 0 ) =/= ; 2 1
2 df-ne
 |-  ( ( 9 + ; 1 0 ) =/= ; 2 1 <-> -. ( 9 + ; 1 0 ) = ; 2 1 )
3 1 2 mpbi
 |-  -. ( 9 + ; 1 0 ) = ; 2 1
4 pm2.21
 |-  ( -. ( 9 + ; 1 0 ) = ; 2 1 -> ( ( 9 + ; 1 0 ) = ; 2 1 -> F (/) ( 0 x. 1 ) ) )
5 3 4 ax-mp
 |-  ( ( 9 + ; 1 0 ) = ; 2 1 -> F (/) ( 0 x. 1 ) )