Metamath Proof Explorer


Theorem inv2

Description: The intersection of the universal class with a class is itself. A commuted form of inv1 . (Contributed by BTernaryTau, 24-Jun-2026)

Ref Expression
Assertion inv2 ( V ∩ 𝐴 ) = 𝐴

Proof

Step Hyp Ref Expression
1 inv1 ( 𝐴 ∩ V ) = 𝐴
2 1 ineqcomi ( V ∩ 𝐴 ) = 𝐴