Theorem wunfv

Description: A weak universe is closed under the function value operator. (Contributed by Mario Carneiro, 3-Jan-2017)

	Ref	Expression
Hypotheses	wun0.1	|- ( ph -> U e. WUni )
	wunop.2	|- ( ph -> A e. U )
Assertion	wunfv	|- ( ph -> ( A ` B ) e. U )

Proof

Step	Hyp	Ref	Expression
1		wun0.1	|- ( ph -> U e. WUni )
2		wunop.2	|- ( ph -> A e. U )
3	1 2	wunrn	|- ( ph -> ran A e. U )
4	1 3	wununi	|- ( ph -> U. ran A e. U )
5		fvssunirn	|- ( A ` B ) C_ U. ran A
6	5	a1i	|- ( ph -> ( A ` B ) C_ U. ran A )
7	1 4 6	wunss	|- ( ph -> ( A ` B ) e. U )