Definition df-cosh 42274

Description: Define the hyperbolic cosine function (cosh). We define it this way for cmpt 4643, which requires the form (𝑥 ∈ 𝐴 ↦ 𝐵). (Contributed by David A. Wheeler, 10-May-2015.)

Assertion

Ref	Expression
df-cosh	⊢ cosh = (𝑥 ∈ ℂ ↦ (cos‘(i · 𝑥)))

Detailed syntax breakdown of Definition df-cosh

Step	Hyp	Ref	Expression
1		ccosh 42271	. 2 class cosh
2		vx	. . 3 setvar 𝑥
3		cc 9813	. . 3 class ℂ
4		ci 9817	. . . . 5 class i
5	2	cv 1474	. . . . 5 class 𝑥
6		cmul 9820	. . . . 5 class ·
7	4, 5, 6	co 6549	. . . 4 class (i · 𝑥)
8		ccos 14634	. . . 4 class cos
9	7, 8	cfv 5804	. . 3 class (cos‘(i · 𝑥))
10	2, 3, 9	cmpt 4643	. 2 class (𝑥 ∈ ℂ ↦ (cos‘(i · 𝑥)))
11	1, 10	wceq 1475	1 wff cosh = (𝑥 ∈ ℂ ↦ (cos‘(i · 𝑥)))

This definition is referenced by:  coshval-named  42277