Theorem dfrel3

Description: Alternate definition of relation. (Contributed by NM, 14-May-2008)

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

Proof

Step	Hyp	Ref	Expression
1		dfrel2	⊢ ( Rel 𝑅 ↔ ◡ ◡ 𝑅 = 𝑅 )
2		cnvcnv2	⊢ ◡ ◡ 𝑅 = ( 𝑅 ↾ V )
3	2	eqeq1i	⊢ ( ◡ ◡ 𝑅 = 𝑅 ↔ ( 𝑅 ↾ V ) = 𝑅 )
4	1 3	bitri	⊢ ( Rel 𝑅 ↔ ( 𝑅 ↾ V ) = 𝑅 )