Definition df-fzo 10113

Description: Define a function generating sets of integers using a half-open range. Read (𝑀..^𝑁) as the integers from 𝑀 up to, but not including, 𝑁; contrast with (𝑀...𝑁) df-fz 9980, which includes 𝑁. Not including the endpoint simplifies a number of formulas related to cardinality and splitting; contrast fzosplit 10147 with fzsplit 10021, for instance. (Contributed by Stefan O'Rear, 14-Aug-2015.)

Assertion

Ref	Expression
df-fzo	⊢ ..^ = (𝑚 ∈ ℤ, 𝑛 ∈ ℤ ↦ (𝑚...(𝑛 − 1)))

Distinct variable group:   𝑚,𝑛

Detailed syntax breakdown of Definition df-fzo

Step	Hyp	Ref	Expression
1		cfzo 10112	. 2 class ..^
2		vm	. . 3 setvar 𝑚
3		vn	. . 3 setvar 𝑛
4		cz 9226	. . 3 class ℤ
5	2	cv 1352	. . . 4 class 𝑚
6	3	cv 1352	. . . . 5 class 𝑛
7		c1 7787	. . . . 5 class 1
8		cmin 8102	. . . . 5 class −
9	6, 7, 8	co 5865	. . . 4 class (𝑛 − 1)
10		cfz 9979	. . . 4 class ...
11	5, 9, 10	co 5865	. . 3 class (𝑚...(𝑛 − 1))
12	2, 3, 4, 4, 11	cmpo 5867	. 2 class (𝑚 ∈ ℤ, 𝑛 ∈ ℤ ↦ (𝑚...(𝑛 − 1)))
13	1, 12	wceq 1353	1 wff ..^ = (𝑚 ∈ ℤ, 𝑛 ∈ ℤ ↦ (𝑚...(𝑛 − 1)))

This definition is referenced by:  fzof  10114  elfzoel1  10115  elfzoel2  10116  fzoval  10118