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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-cosh | Structured version Visualization version GIF version |
Description: Define the hyperbolic cosine function (cosh). We define it this way for cmpt 5135, which requires the form (𝑥 ∈ 𝐴 ↦ 𝐵). (Contributed by David A. Wheeler, 10-May-2015.) |
Ref | Expression |
---|---|
df-cosh | ⊢ cosh = (𝑥 ∈ ℂ ↦ (cos‘(i · 𝑥))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ccosh 46104 | . 2 class cosh | |
2 | vx | . . 3 setvar 𝑥 | |
3 | cc 10727 | . . 3 class ℂ | |
4 | ci 10731 | . . . . 5 class i | |
5 | 2 | cv 1542 | . . . . 5 class 𝑥 |
6 | cmul 10734 | . . . . 5 class · | |
7 | 4, 5, 6 | co 7213 | . . . 4 class (i · 𝑥) |
8 | ccos 15626 | . . . 4 class cos | |
9 | 7, 8 | cfv 6380 | . . 3 class (cos‘(i · 𝑥)) |
10 | 2, 3, 9 | cmpt 5135 | . 2 class (𝑥 ∈ ℂ ↦ (cos‘(i · 𝑥))) |
11 | 1, 10 | wceq 1543 | 1 wff cosh = (𝑥 ∈ ℂ ↦ (cos‘(i · 𝑥))) |
Colors of variables: wff setvar class |
This definition is referenced by: coshval-named 46110 |
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