Definition df-fzo 9153

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 9030, which includes 𝑁. Not including the endpoint simplifies a number of formulae related to cardinality and splitting; contrast fzosplit 9186 with fzsplit 9070, 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 9152	. 2 class ..^
2		vm	. . 3 setvar 𝑚
3		vn	. . 3 setvar 𝑛
4		cz 8351	. . 3 class ℤ
5	2	cv 1283	. . . 4 class 𝑚
6	3	cv 1283	. . . . 5 class 𝑛
7		c1 6982	. . . . 5 class 1
8		cmin 7279	. . . . 5 class −
9	6, 7, 8	co 5532	. . . 4 class (𝑛 − 1)
10		cfz 9029	. . . 4 class ...
11	5, 9, 10	co 5532	. . 3 class (𝑚...(𝑛 − 1))
12	2, 3, 4, 4, 11	cmpt2 5534	. 2 class (𝑚 ∈ ℤ, 𝑛 ∈ ℤ ↦ (𝑚...(𝑛 − 1)))
13	1, 12	wceq 1284	1 wff ..^ = (𝑚 ∈ ℤ, 𝑛 ∈ ℤ ↦ (𝑚...(𝑛 − 1)))

This definition is referenced by:  fzof  9154  elfzoel1  9155  elfzoel2  9156  fzoval  9158