Theorem wunpm

Description: A weak universe is closed under partial 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	wunpm	|- ( ph -> ( A ^pm 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 3 2	wunxp	|- ( ph -> ( B X. A ) e. U )
5	1 4	wunpw	|- ( ph -> ~P ( B X. A ) e. U )
6		pmsspw	|- ( A ^pm B ) C_ ~P ( B X. A )
7	6	a1i	|- ( ph -> ( A ^pm B ) C_ ~P ( B X. A ) )
8	1 5 7	wunss	|- ( ph -> ( A ^pm B ) e. U )