Theorem inex2g

Description: Sufficient condition for an intersection to be a set. Commuted form of inex1g . (Contributed by Peter Mazsa, 19-Dec-2018)

	Ref	Expression
Assertion	inex2g	⊢ ( 𝐴 ∈ 𝑉 → ( 𝐵 ∩ 𝐴 ) ∈ V )

Proof

Step	Hyp	Ref	Expression
1		incom	⊢ ( 𝐵 ∩ 𝐴 ) = ( 𝐴 ∩ 𝐵 )
2		inex1g	⊢ ( 𝐴 ∈ 𝑉 → ( 𝐴 ∩ 𝐵 ) ∈ V )
3	1 2	eqeltrid	⊢ ( 𝐴 ∈ 𝑉 → ( 𝐵 ∩ 𝐴 ) ∈ V )