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Definition df-cosh 41794
Description: Define the hyperbolic cosine function (cosh). We define it this way for cmpt 4678, which requires the form (𝑥𝐴𝐵). (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
StepHypRef Expression
1 ccosh 41791 . 2 class cosh
2 vx . . 3 setvar 𝑥
3 cc 9886 . . 3 class
4 ci 9890 . . . . 5 class i
52cv 1479 . . . . 5 class 𝑥
6 cmul 9893 . . . . 5 class ·
74, 5, 6co 6610 . . . 4 class (i · 𝑥)
8 ccos 14731 . . . 4 class cos
97, 8cfv 5852 . . 3 class (cos‘(i · 𝑥))
102, 3, 9cmpt 4678 . 2 class (𝑥 ∈ ℂ ↦ (cos‘(i · 𝑥)))
111, 10wceq 1480 1 wff cosh = (𝑥 ∈ ℂ ↦ (cos‘(i · 𝑥)))
Colors of variables: wff setvar class
This definition is referenced by:  coshval-named  41797
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