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Definition df-naryf 47313
Description: Define the n-ary (endo)functions. (Contributed by AV, 11-May-2024.) (Revised by TA and SN, 7-Jun-2024.)
Assertion
Ref Expression
df-naryf -aryF = (𝑛 ∈ ℕ0, 𝑥 ∈ V ↦ (𝑥m (𝑥m (0..^𝑛))))
Distinct variable group:   𝑥,𝑛

Detailed syntax breakdown of Definition df-naryf
StepHypRef Expression
1 cnaryf 47312 . 2 class -aryF
2 vn . . 3 setvar 𝑛
3 vx . . 3 setvar 𝑥
4 cn0 12472 . . 3 class 0
5 cvv 3475 . . 3 class V
63cv 1541 . . . 4 class 𝑥
7 cc0 11110 . . . . . 6 class 0
82cv 1541 . . . . . 6 class 𝑛
9 cfzo 13627 . . . . . 6 class ..^
107, 8, 9co 7409 . . . . 5 class (0..^𝑛)
11 cmap 8820 . . . . 5 class m
126, 10, 11co 7409 . . . 4 class (𝑥m (0..^𝑛))
136, 12, 11co 7409 . . 3 class (𝑥m (𝑥m (0..^𝑛)))
142, 3, 4, 5, 13cmpo 7411 . 2 class (𝑛 ∈ ℕ0, 𝑥 ∈ V ↦ (𝑥m (𝑥m (0..^𝑛))))
151, 14wceq 1542 1 wff -aryF = (𝑛 ∈ ℕ0, 𝑥 ∈ V ↦ (𝑥m (𝑥m (0..^𝑛))))
Colors of variables: wff setvar class
This definition is referenced by:  naryfval  47314  naryfvalixp  47315  naryrcl  47317  1aryenef  47331  2aryenef  47342
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