Theorem wuntp

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

	Ref	Expression
Hypotheses	wununi.1	|- ( ph -> U e. WUni )
	wununi.2	|- ( ph -> A e. U )
	wunpr.3	|- ( ph -> B e. U )
	wuntp.3	|- ( ph -> C e. U )
Assertion	wuntp	|- ( ph -> { A , B , C } e. U )

Proof

Step	Hyp	Ref	Expression
1		wununi.1	|- ( ph -> U e. WUni )
2		wununi.2	|- ( ph -> A e. U )
3		wunpr.3	|- ( ph -> B e. U )
4		wuntp.3	|- ( ph -> C e. U )
5		tpass	|- { A , B , C } = ( { A } u. { B , C } )
6		dfsn2	|- { A } = { A , A }
7	1 2 2	wunpr	|- ( ph -> { A , A } e. U )
8	6 7	eqeltrid	|- ( ph -> { A } e. U )
9	1 3 4	wunpr	|- ( ph -> { B , C } e. U )
10	1 8 9	wunun	|- ( ph -> ( { A } u. { B , C } ) e. U )
11	5 10	eqeltrid	|- ( ph -> { A , B , C } e. U )