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 · 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 · 1 ) ) )
5	3 4	ax-mp	⊢ ( ( 9 + ; 1 0 ) = ; 2 1 → 𝐹 ∅ ( 0 · 1 ) )