Theorem wunin

Description: A weak universe is closed under binary intersections. (Contributed by Mario Carneiro, 2-Jan-2017)

	Ref	Expression
Hypotheses	wununi.1	$$⊢\phi \to U\in \mathrm{WUni}$$
	wununi.2	$$⊢\phi \to A\in U$$
Assertion	wunin	$$⊢\phi \to A\cap B\in U$$

Proof

Step	Hyp	Ref	Expression
1		wununi.1	$$⊢\phi \to U\in \mathrm{WUni}$$
2		wununi.2	$$⊢\phi \to A\in U$$
3		inss1	$$⊢A\cap B\subseteq A$$
4	3	a1i	$$⊢\phi \to A\cap B\subseteq A$$
5	1 2 4	wunss	$$⊢\phi \to A\cap B\in U$$