Theorem inex3

Description: Sufficient condition for the intersection relation to be a set. (Contributed by Peter Mazsa, 24-Nov-2019)

	Ref	Expression
Assertion	inex3	⊢ ( ( 𝐴 ∈ 𝑉 ∨ 𝐵 ∈ 𝑊 ) → ( 𝐴 ∩ 𝐵 ) ∈ V )

Proof

Step	Hyp	Ref	Expression
1		inex1g	⊢ ( 𝐴 ∈ 𝑉 → ( 𝐴 ∩ 𝐵 ) ∈ V )
2		inex2g	⊢ ( 𝐵 ∈ 𝑊 → ( 𝐴 ∩ 𝐵 ) ∈ V )
3	1 2	jaoi	⊢ ( ( 𝐴 ∈ 𝑉 ∨ 𝐵 ∈ 𝑊 ) → ( 𝐴 ∩ 𝐵 ) ∈ V )