Theorem funresd

Description: A restriction of a function is a function. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypothesis	funresd.1	$$⊢\phi \to \mathrm{Fun}F$$
Assertion	funresd	$$⊢\phi \to \mathrm{Fun}\left({F\upharpoonright }_A\right)$$

Proof

Step	Hyp	Ref	Expression
1		funresd.1	$$⊢\phi \to \mathrm{Fun}F$$
2		funres	$$⊢\mathrm{Fun}F\to \mathrm{Fun}\left({F\upharpoonright }_A\right)$$
3	1 2	syl	$$⊢\phi \to \mathrm{Fun}\left({F\upharpoonright }_A\right)$$