Theorem wunin

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

	Ref	Expression
Hypotheses	wununi.1	|- ( ph -> U e. WUni )
	wununi.2	|- ( ph -> A e. U )
Assertion	wunin	|- ( ph -> ( A i^i B ) e. U )

Proof

Step	Hyp	Ref	Expression
1		wununi.1	|- ( ph -> U e. WUni )
2		wununi.2	|- ( ph -> A e. U )
3		inss1	|- ( A i^i B ) C_ A
4	3	a1i	|- ( ph -> ( A i^i B ) C_ A )
5	1 2 4	wunss	|- ( ph -> ( A i^i B ) e. U )