Theorem wunmap

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

	Ref	Expression
Hypotheses	wun0.1	|- ( ph -> U e. WUni )
	wunop.2	|- ( ph -> A e. U )
	wunop.3	|- ( ph -> B e. U )
Assertion	wunmap	|- ( ph -> ( A ^m B ) e. U )

Proof

Step	Hyp	Ref	Expression
1		wun0.1	|- ( ph -> U e. WUni )
2		wunop.2	|- ( ph -> A e. U )
3		wunop.3	|- ( ph -> B e. U )
4	1 2 3	wunpm	|- ( ph -> ( A ^pm B ) e. U )
5		mapsspm	|- ( A ^m B ) C_ ( A ^pm B )
6	5	a1i	|- ( ph -> ( A ^m B ) C_ ( A ^pm B ) )
7	1 4 6	wunss	|- ( ph -> ( A ^m B ) e. U )