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	⊢ ( 𝜑 → 𝑈 ∈ WUni )
	1strwun.o	⊢ ( 𝜑 → ω ∈ 𝑈 )
Assertion	1strwun	⊢ ( ( 𝜑 ∧ 𝐵 ∈ 𝑈 ) → 𝐺 ∈ 𝑈 )

Proof

Step	Hyp	Ref	Expression
1		1str.g	⊢ 𝐺 = { ⟨ ( Base ‘ ndx ) , 𝐵 ⟩ }
2		1strwun.u	⊢ ( 𝜑 → 𝑈 ∈ WUni )
3		1strwun.o	⊢ ( 𝜑 → ω ∈ 𝑈 )
4	2 3	basndxelwund	⊢ ( 𝜑 → ( Base ‘ ndx ) ∈ 𝑈 )
5	1 2 4	1strwunbndx	⊢ ( ( 𝜑 ∧ 𝐵 ∈ 𝑈 ) → 𝐺 ∈ 𝑈 )