Theorem bj-dfrel3

Description: Alternate definition of relation: a class is a relation if and only if it is equal to its "relation part" (see relpart ). (Contributed by NM, 14-May-2008) Do not depend on df-cnv to move it earlier. (Revised by BJ, 16-Oct-2026)

	Ref	Expression
Assertion	bj-dfrel3	⊢ ( Rel 𝑅 ↔ ( 𝑅 ↾ V ) = 𝑅 )

Proof

Step	Hyp	Ref	Expression
1		df-rel	⊢ ( Rel 𝑅 ↔ 𝑅 ⊆ ( V × V ) )
2		bj-resssxp	⊢ ( ( 𝑅 ↾ V ) = 𝑅 ↔ 𝑅 ⊆ ( V × V ) )
3	1 2	bitr4i	⊢ ( Rel 𝑅 ↔ ( 𝑅 ↾ V ) = 𝑅 )