Definition df-fmtno 47542

Description: Define the function that enumerates the Fermat numbers, see definition in [ApostolNT] p. 7. (Contributed by AV, 13-Jun-2021.)

Assertion

Ref	Expression
df-fmtno	⊢ FermatNo = (𝑛 ∈ ℕ0 ↦ ((2↑(2↑𝑛)) + 1))

Detailed syntax breakdown of Definition df-fmtno

Step	Hyp	Ref	Expression
1		cfmtno 47541	. 2 class FermatNo
2		vn	. . 3 setvar 𝑛
3		cn0 12501	. . 3 class ℕ0
4		c2 12295	. . . . 5 class 2
5	2	cv 1539	. . . . . 6 class 𝑛
6		cexp 14079	. . . . . 6 class ↑
7	4, 5, 6	co 7405	. . . . 5 class (2↑𝑛)
8	4, 7, 6	co 7405	. . . 4 class (2↑(2↑𝑛))
9		c1 11130	. . . 4 class 1
10		caddc 11132	. . . 4 class +
11	8, 9, 10	co 7405	. . 3 class ((2↑(2↑𝑛)) + 1)
12	2, 3, 11	cmpt 5201	. 2 class (𝑛 ∈ ℕ0 ↦ ((2↑(2↑𝑛)) + 1))
13	1, 12	wceq 1540	1 wff FermatNo = (𝑛 ∈ ℕ0 ↦ ((2↑(2↑𝑛)) + 1))

This definition is referenced by:  fmtno  47543  fmtnorn  47548  fmtnof1  47549  fmtnodvds  47558