Theorem ffvelrnda

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

	Ref	Expression
Hypothesis	ffvelrnd.1	|- ( ph -> F : A --> B )
Assertion	ffvelrnda	|- ( ( ph /\ C e. A ) -> ( F ` C ) e. B )

Proof

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