Metamath Proof Explorer


Theorem nprrel12

Description: Proper classes are not related via any relation. (Contributed by AV, 29-Oct-2021)

Ref Expression
Hypothesis nprrel12.1
|- Rel R
Assertion nprrel12
|- ( -. ( A e. _V /\ B e. _V ) -> -. A R B )

Proof

Step Hyp Ref Expression
1 nprrel12.1
 |-  Rel R
2 1 brrelex12i
 |-  ( A R B -> ( A e. _V /\ B e. _V ) )
3 2 con3i
 |-  ( -. ( A e. _V /\ B e. _V ) -> -. A R B )