Metamath Proof Explorer


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