Theorem 1strwun

Description: A constructed one-slot structure in a weak universe. (Contributed by AV, 27-Mar-2020) (Proof shortened by AV, 17-Oct-2024)

	Ref	Expression
Hypotheses	1str.g	|- G = { <. ( Base ` ndx ) , B >. }
	1strwun.u	|- ( ph -> U e. WUni )
	1strwun.o	|- ( ph -> _om e. U )
Assertion	1strwun	|- ( ( ph /\ B e. U ) -> G e. U )

Proof

Step	Hyp	Ref	Expression
1		1str.g	|- G = { <. ( Base ` ndx ) , B >. }
2		1strwun.u	|- ( ph -> U e. WUni )
3		1strwun.o	|- ( ph -> _om e. U )
4	2 3	basndxelwund	|- ( ph -> ( Base ` ndx ) e. U )
5	1 2 4	1strwunbndx	|- ( ( ph /\ B e. U ) -> G e. U )