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Definition df-sinh 47856
Description: Define the hyperbolic sine function (sinh). We define it this way for cmpt 5231, which requires the form (π‘₯ ∈ 𝐴 ↦ 𝐡). See sinhval-named 47859 for a simple way to evaluate it. We define this function by dividing by i, which uses fewer operations than many conventional definitions (and thus is more convenient to use in set.mm). See sinh-conventional 47862 for a justification that our definition is the same as the conventional definition of sinh used in other sources. (Contributed by David A. Wheeler, 20-Apr-2015.)
Assertion
Ref Expression
df-sinh sinh = (π‘₯ ∈ β„‚ ↦ ((sinβ€˜(i Β· π‘₯)) / i))

Detailed syntax breakdown of Definition df-sinh
StepHypRef Expression
1 csinh 47853 . 2 class sinh
2 vx . . 3 setvar π‘₯
3 cc 11110 . . 3 class β„‚
4 ci 11114 . . . . . 6 class i
52cv 1540 . . . . . 6 class π‘₯
6 cmul 11117 . . . . . 6 class Β·
74, 5, 6co 7411 . . . . 5 class (i Β· π‘₯)
8 csin 16009 . . . . 5 class sin
97, 8cfv 6543 . . . 4 class (sinβ€˜(i Β· π‘₯))
10 cdiv 11873 . . . 4 class /
119, 4, 10co 7411 . . 3 class ((sinβ€˜(i Β· π‘₯)) / i)
122, 3, 11cmpt 5231 . 2 class (π‘₯ ∈ β„‚ ↦ ((sinβ€˜(i Β· π‘₯)) / i))
131, 12wceq 1541 1 wff sinh = (π‘₯ ∈ β„‚ ↦ ((sinβ€˜(i Β· π‘₯)) / i))
Colors of variables: wff setvar class
This definition is referenced by:  sinhval-named  47859
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