Metamath Proof Explorer


Theorem elopabr

Description: Membership in an ordered-pair class abstraction defined by a binary relation. (Contributed by AV, 16-Feb-2021) (Proof shortened by SN, 11-Dec-2024)

Ref Expression
Assertion elopabr
|- ( A e. { <. x , y >. | x R y } -> A e. R )

Proof

Step Hyp Ref Expression
1 opabss
 |-  { <. x , y >. | x R y } C_ R
2 1 sseli
 |-  ( A e. { <. x , y >. | x R y } -> A e. R )