Theorem ffvelcdmd

Description: A function's value belongs to its codomain. (Contributed by Mario Carneiro, 29-Dec-2016)

	Ref	Expression
Hypotheses	ffvelcdmd.1	|- ( ph -> F : A --> B )
	ffvelcdmd.2	|- ( ph -> C e. A )
Assertion	ffvelcdmd	|- ( ph -> ( F ` C ) e. B )

Proof

Step	Hyp	Ref	Expression
1		ffvelcdmd.1	|- ( ph -> F : A --> B )
2		ffvelcdmd.2	|- ( ph -> C e. A )
3	1	ffvelcdmda	|- ( ( ph /\ C e. A ) -> ( F ` C ) e. B )
4	2 3	mpdan	|- ( ph -> ( F ` C ) e. B )