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Metamath Proof Explorer

Theorem ffvelcdmda

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

		Ref	Expression
	Hypothesis	ffvelcdmd.1	$⊢ φ \to F : A ⟶ B$
	Assertion	ffvelcdmda	$⊢ (φ \land C \in A) \to F (C) \in B$

Step	Hyp	Ref	Expression
1		ffvelcdmd.1	$⊢ φ \to F : A ⟶ B$
2		ffvelcdm	$⊢ (F : A ⟶ B \land C \in A) \to F (C) \in B$
3	1 2	sylan	$⊢ (φ \land C \in A) \to F (C) \in B$