Metamath Proof Explorer


Theorem cnpf

Description: A continuous function at point P is a mapping. (Contributed by FL, 17-Nov-2006) (Revised by Mario Carneiro, 21-Aug-2015)

Ref Expression
Hypotheses iscnp2.1 X = J
iscnp2.2 Y = K
Assertion cnpf F J CnP K P F : X Y

Proof

Step Hyp Ref Expression
1 iscnp2.1 X = J
2 iscnp2.2 Y = K
3 1 2 iscnp2 F J CnP K P J Top K Top P X F : X Y y K F P y x J P x F x y
4 3 simprbi F J CnP K P F : X Y y K F P y x J P x F x y
5 4 simpld F J CnP K P F : X Y