Theorem bj-cnvcnv2

Description: The double converse of a class equals its restriction to the universe. (Contributed by NM, 8-Oct-2007) Do not depend on cnvcnv in order to prove it from cnvcnv2 . (Revised by BJ, 16-Oct-2026) Do not depend on cnvcnv . (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-cnvcnv2	⊢ ◡ ◡ 𝐴 = ( 𝐴 ↾ V )

Proof

Step	Hyp	Ref	Expression
1		cnvcnv3	⊢ ◡ ◡ 𝐴 = { ⟨ 𝑥 , 𝑦 ⟩ ∣ 𝑥 𝐴 𝑦 }
2		relpart	⊢ ( 𝐴 ↾ V ) = { ⟨ 𝑥 , 𝑦 ⟩ ∣ 𝑥 𝐴 𝑦 }
3	1 2	eqtr4i	⊢ ◡ ◡ 𝐴 = ( 𝐴 ↾ V )