Metamath Proof Explorer

Theorem recoshcl

Description: The hyperbolic cosine of a real number is real. (Contributed by Mario Carneiro, 4-Apr-2015)

Ref Expression
Assertion recoshcl 
|- ( A e. RR -> ( cos ` ( _i x. A ) ) e. RR )

Proof

Step Hyp Ref Expression
1 rpcoshcl 
 |-  ( A e. RR -> ( cos ` ( _i x. A ) ) e. RR+ )
2 1 rpred 
 |-  ( A e. RR -> ( cos ` ( _i x. A ) ) e. RR )