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Definition df-fzo 9000
 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 8875, which includes 𝑁. Not including the endpoint simplifies a number of formulae related to cardinality and splitting; contrast fzosplit 9033 with fzsplit 8915, 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 8999 . 2 class ..^
2 vm . . 3 setvar 𝑚
3 vn . . 3 setvar 𝑛
4 cz 8245 . . 3 class
52cv 1242 . . . 4 class 𝑚
63cv 1242 . . . . 5 class 𝑛
7 c1 6890 . . . . 5 class 1
8 cmin 7182 . . . . 5 class
96, 7, 8co 5512 . . . 4 class (𝑛 − 1)
10 cfz 8874 . . . 4 class ...
115, 9, 10co 5512 . . 3 class (𝑚...(𝑛 − 1))
122, 3, 4, 4, 11cmpt2 5514 . 2 class (𝑚 ∈ ℤ, 𝑛 ∈ ℤ ↦ (𝑚...(𝑛 − 1)))
131, 12wceq 1243 1 wff ..^ = (𝑚 ∈ ℤ, 𝑛 ∈ ℤ ↦ (𝑚...(𝑛 − 1)))
 Colors of variables: wff set class This definition is referenced by:  fzof  9001  elfzoel1  9002  elfzoel2  9003  fzoval  9005
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