Theorem wunres

Description: A weak universe is closed under restrictions. (Contributed by Mario Carneiro, 12-Jan-2017)

	Ref	Expression
Hypotheses	wun0.1	$$⊢\phi \to U\in \mathrm{WUni}$$
	wunop.2	$$⊢\phi \to A\in U$$
Assertion	wunres	$$⊢\phi \to {A\upharpoonright }_B\in U$$

Proof

Step	Hyp	Ref	Expression
1		wun0.1	$$⊢\phi \to U\in \mathrm{WUni}$$
2		wunop.2	$$⊢\phi \to A\in U$$
3		resss	$$⊢{A\upharpoonright }_B\subseteq A$$
4	3	a1i	$$⊢\phi \to {A\upharpoonright }_B\subseteq A$$
5	1 2 4	wunss	$$⊢\phi \to {A\upharpoonright }_B\in U$$