Theorem fovcdmd

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

	Ref	Expression
Hypotheses	fovcdmd.1	$$⊢\phi \to F:R\times S⟶C$$
	fovcdmd.2	$$⊢\phi \to A\in R$$
	fovcdmd.3	$$⊢\phi \to B\in S$$
Assertion	fovcdmd	$$⊢\phi \to AFB\in C$$

Proof

Step	Hyp	Ref	Expression
1		fovcdmd.1	$$⊢\phi \to F:R\times S⟶C$$
2		fovcdmd.2	$$⊢\phi \to A\in R$$
3		fovcdmd.3	$$⊢\phi \to B\in S$$
4		fovcdm	$$⊢\left(F:R\times S⟶C\wedge A\in R\wedge B\in S\right)\to AFB\in C$$
5	1 2 3 4	syl3anc	$$⊢\phi \to AFB\in C$$