Theorem frnd

Description: Deduction form of frn . The range of a mapping. (Contributed by Glauco Siliprandi, 26-Jun-2021)

	Ref	Expression
Hypothesis	frnd.1	$$⊢\phi \to F:A⟶B$$
Assertion	frnd	$$⊢\phi \to \mathrm{ran}F\subseteq B$$

Proof

Step	Hyp	Ref	Expression
1		frnd.1	$$⊢\phi \to F:A⟶B$$
2		frn	$$⊢F:A⟶B\to \mathrm{ran}F\subseteq B$$
3	1 2	syl	$$⊢\phi \to \mathrm{ran}F\subseteq B$$