Theorem wuncnv

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

	Ref	Expression
Hypotheses	wun0.1	|- ( ph -> U e. WUni )
	wunop.2	|- ( ph -> A e. U )
Assertion	wuncnv	|- ( ph -> `' A 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 2	wundm	|- ( ph -> dom A e. U )
5	1 3 4	wunxp	|- ( ph -> ( ran A X. dom A ) e. U )
6		cnvssrndm	|- `' A C_ ( ran A X. dom A )
7	6	a1i	|- ( ph -> `' A C_ ( ran A X. dom A ) )
8	1 5 7	wunss	|- ( ph -> `' A e. U )