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	$$⊢A\in \left\{⟨x,y⟩|xRy\right\}\to A\in R$$

Proof

Step	Hyp	Ref	Expression
1		opabss	$$⊢\left\{⟨x,y⟩|xRy\right\}\subseteq R$$
2	1	sseli	$$⊢A\in \left\{⟨x,y⟩|xRy\right\}\to A\in R$$