Theorem wunss

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

	Ref	Expression
Hypotheses	wununi.1	|- ( ph -> U e. WUni )
	wununi.2	|- ( ph -> A e. U )
	wunss.3	|- ( ph -> B C_ A )
Assertion	wunss	|- ( ph -> B e. U )

Proof

Step	Hyp	Ref	Expression
1		wununi.1	|- ( ph -> U e. WUni )
2		wununi.2	|- ( ph -> A e. U )
3		wunss.3	|- ( ph -> B C_ A )
4	1 2	wunpw	|- ( ph -> ~P A e. U )
5	1 4	wunelss	|- ( ph -> ~P A C_ U )
6	2 3	sselpwd	|- ( ph -> B e. ~P A )
7	5 6	sseldd	|- ( ph -> B e. U )