Description: Value of the named cosh function. Here we show the simple conversion to the conventional form used in set.mm, using the definition given by df-cosh . See coshval for a theorem to convert this further. (Contributed by David A. Wheeler, 10-May-2015)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | coshval-named | |- ( A e. CC -> ( cosh ` A ) = ( cos ` ( _i x. A ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | oveq2 | |- ( x = A -> ( _i x. x ) = ( _i x. A ) ) |
|
| 2 | 1 | fveq2d | |- ( x = A -> ( cos ` ( _i x. x ) ) = ( cos ` ( _i x. A ) ) ) |
| 3 | df-cosh | |- cosh = ( x e. CC |-> ( cos ` ( _i x. x ) ) ) |
|
| 4 | fvex | |- ( cos ` ( _i x. A ) ) e. _V |
|
| 5 | 2 3 4 | fvmpt | |- ( A e. CC -> ( cosh ` A ) = ( cos ` ( _i x. A ) ) ) |