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Definition df-fzo 12423
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 12285, which includes 𝑁. Not including the endpoint simplifies a number of formulae related to cardinality and splitting; contrast fzosplit 12458 with fzsplit 12325, 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
StepHypRef Expression
1 cfzo 12422 . 2 class ..^
2 vm . . 3 setvar 𝑚
3 vn . . 3 setvar 𝑛
4 cz 11337 . . 3 class
52cv 1479 . . . 4 class 𝑚
63cv 1479 . . . . 5 class 𝑛
7 c1 9897 . . . . 5 class 1
8 cmin 10226 . . . . 5 class
96, 7, 8co 6615 . . . 4 class (𝑛 − 1)
10 cfz 12284 . . . 4 class ...
115, 9, 10co 6615 . . 3 class (𝑚...(𝑛 − 1))
122, 3, 4, 4, 11cmpt2 6617 . 2 class (𝑚 ∈ ℤ, 𝑛 ∈ ℤ ↦ (𝑚...(𝑛 − 1)))
131, 12wceq 1480 1 wff ..^ = (𝑚 ∈ ℤ, 𝑛 ∈ ℤ ↦ (𝑚...(𝑛 − 1)))
Colors of variables: wff setvar class
This definition is referenced by:  fzof  12424  fzoval  12428
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