Theorem ffvelrnd

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

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

Proof

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