Theorem wunres

Description: A weak universe is closed under restrictions. (Contributed by Mario Carneiro, 12-Jan-2017)

	Ref	Expression
Hypotheses	wun0.1	⊢ ( 𝜑 → 𝑈 ∈ WUni )
	wunop.2	⊢ ( 𝜑 → 𝐴 ∈ 𝑈 )
Assertion	wunres	⊢ ( 𝜑 → ( 𝐴 ↾ 𝐵 ) ∈ 𝑈 )

Proof

Step	Hyp	Ref	Expression
1		wun0.1	⊢ ( 𝜑 → 𝑈 ∈ WUni )
2		wunop.2	⊢ ( 𝜑 → 𝐴 ∈ 𝑈 )
3		resss	⊢ ( 𝐴 ↾ 𝐵 ) ⊆ 𝐴
4	3	a1i	⊢ ( 𝜑 → ( 𝐴 ↾ 𝐵 ) ⊆ 𝐴 )
5	1 2 4	wunss	⊢ ( 𝜑 → ( 𝐴 ↾ 𝐵 ) ∈ 𝑈 )