Theorem wunsn

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

	Ref	Expression
Hypotheses	wununi.1	|- ( ph -> U e. WUni )
	wununi.2	|- ( ph -> A e. U )
Assertion	wunsn	|- ( ph -> { A } e. U )

Proof

Step	Hyp	Ref	Expression
1		wununi.1	|- ( ph -> U e. WUni )
2		wununi.2	|- ( ph -> A e. U )
3		dfsn2	|- { A } = { A , A }
4	1 2 2	wunpr	|- ( ph -> { A , A } e. U )
5	3 4	eqeltrid	|- ( ph -> { A } e. U )