Theorem wunsn

Description: A weak universe is closed under singletons. (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	wunsn	$$⊢\phi \to \left\{A\right\}\in U$$

Proof

Step	Hyp	Ref	Expression
1		wununi.1	$$⊢\phi \to U\in \mathrm{WUni}$$
2		wununi.2	$$⊢\phi \to A\in U$$
3		dfsn2	$$⊢\left\{A\right\}=\left\{A,A\right\}$$
4	1 2 2	wunpr	$$⊢\phi \to \left\{A,A\right\}\in U$$
5	3 4	eqeltrid	$$⊢\phi \to \left\{A\right\}\in U$$