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	$$⊢9+10=21\to F\varnothing 0\cdot 1$$

Proof

Step	Hyp	Ref	Expression
1		9p10ne21	$$⊢9+10\ne 21$$
2		df-ne	$$⊢9+10\ne 21\leftrightarrow \neg 9+10=21$$
3	1 2	mpbi	$$⊢\neg 9+10=21$$
4		pm2.21	$$⊢\neg 9+10=21\to \left(9+10=21\to F\varnothing 0\cdot 1\right)$$
5	3 4	ax-mp	$$⊢9+10=21\to F\varnothing 0\cdot 1$$