Theorem fzo12sn

Description: A 1-based half-open integer interval up to, but not including, 2 is a singleton. (Contributed by Alexander van der Vekens, 31-Jan-2018)

	Ref	Expression
Assertion	fzo12sn	$$⊢\left(1..^2\right)=\left\{1\right\}$$

Proof

Step	Hyp	Ref	Expression
1		df-2	$$⊢2=1+1$$
2	1	oveq2i	$$⊢\left(1..^2\right)=\left(1..^1+1\right)$$
3		1z	$$⊢1\in \mathbb{Z}$$
4		fzosn	$$⊢1\in \mathbb{Z}\to \left(1..^1+1\right)=\left\{1\right\}$$
5	3 4	ax-mp	$$⊢\left(1..^1+1\right)=\left\{1\right\}$$
6	2 5	eqtri	$$⊢\left(1..^2\right)=\left\{1\right\}$$