Theorem fvi

Description: The value of the identity function. (Contributed by NM, 1-May-2004) (Revised by Mario Carneiro, 28-Apr-2015)

	Ref	Expression
Assertion	fvi	⊢ ( 𝐴 ∈ 𝑉 → ( I ‘ 𝐴 ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		funi	⊢ Fun I
2		ididg	⊢ ( 𝐴 ∈ 𝑉 → 𝐴 I 𝐴 )
3		funbrfv	⊢ ( Fun I → ( 𝐴 I 𝐴 → ( I ‘ 𝐴 ) = 𝐴 ) )
4	1 2 3	mpsyl	⊢ ( 𝐴 ∈ 𝑉 → ( I ‘ 𝐴 ) = 𝐴 )