Metamath Proof Explorer


Theorem elopabrOLD

Description: Obsolete version of elopabr as of 11-Dec-2024. (Contributed by AV, 16-Feb-2021) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion elopabrOLD A x y | x R y A R

Proof

Step Hyp Ref Expression
1 elopab A x y | x R y x y A = x y x R y
2 df-br x R y x y R
3 2 biimpi x R y x y R
4 eleq1 A = x y A R x y R
5 3 4 imbitrrid A = x y x R y A R
6 5 imp A = x y x R y A R
7 6 exlimivv x y A = x y x R y A R
8 1 7 sylbi A x y | x R y A R