Theorem fssd

Description: Expanding the codomain of a mapping, deduction form. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Hypotheses	fssd.f	$$⊢\phi \to F:A⟶B$$
	fssd.b	$$⊢\phi \to B\subseteq C$$
Assertion	fssd	$$⊢\phi \to F:A⟶C$$

Proof

Step	Hyp	Ref	Expression
1		fssd.f	$$⊢\phi \to F:A⟶B$$
2		fssd.b	$$⊢\phi \to B\subseteq C$$
3		fss	$$⊢\left(F:A⟶B\wedge B\subseteq C\right)\to F:A⟶C$$
4	1 2 3	syl2anc	$$⊢\phi \to F:A⟶C$$