Definition df-naryf 47391

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 ↦ (𝑥 ↑m (𝑥 ↑m (0..^𝑛))))

Distinct variable group:   𝑥,𝑛

Detailed syntax breakdown of Definition df-naryf

Step	Hyp	Ref	Expression
1		cnaryf 47390	. 2 class -aryF
2		vn	. . 3 setvar 𝑛
3		vx	. . 3 setvar 𝑥
4		cn0 12474	. . 3 class ℕ0
5		cvv 3474	. . 3 class V
6	3	cv 1540	. . . 4 class 𝑥
7		cc0 11112	. . . . . 6 class 0
8	2	cv 1540	. . . . . 6 class 𝑛
9		cfzo 13629	. . . . . 6 class ..^
10	7, 8, 9	co 7411	. . . . 5 class (0..^𝑛)
11		cmap 8822	. . . . 5 class ↑m
12	6, 10, 11	co 7411	. . . 4 class (𝑥 ↑m (0..^𝑛))
13	6, 12, 11	co 7411	. . 3 class (𝑥 ↑m (𝑥 ↑m (0..^𝑛)))
14	2, 3, 4, 5, 13	cmpo 7413	. 2 class (𝑛 ∈ ℕ0, 𝑥 ∈ V ↦ (𝑥 ↑m (𝑥 ↑m (0..^𝑛))))
15	1, 14	wceq 1541	1 wff -aryF = (𝑛 ∈ ℕ0, 𝑥 ∈ V ↦ (𝑥 ↑m (𝑥 ↑m (0..^𝑛))))

This definition is referenced by:  naryfval  47392  naryfvalixp  47393  naryrcl  47395  1aryenef  47409  2aryenef  47420