Theorem wunres

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

	Ref	Expression
Hypotheses	wun0.1	|- ( ph -> U e. WUni )
	wunop.2	|- ( ph -> A e. U )
Assertion	wunres	|- ( ph -> ( A |` B ) e. U )

Proof

Step	Hyp	Ref	Expression
1		wun0.1	|- ( ph -> U e. WUni )
2		wunop.2	|- ( ph -> A e. U )
3		resss	|- ( A |` B ) C_ A
4	3	a1i	|- ( ph -> ( A |` B ) C_ A )
5	1 2 4	wunss	|- ( ph -> ( A |` B ) e. U )