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	$$⊢A\in V\to \mathrm{I}\left(A\right)=A$$

Proof

Step	Hyp	Ref	Expression
1		funi	$$⊢\mathrm{Fun}\mathrm{I}$$
2		ididg	$$⊢A\in V\to A\mathrm{I}A$$
3		funbrfv	$$⊢\mathrm{Fun}\mathrm{I}\to \left(A\mathrm{I}A\to \mathrm{I}\left(A\right)=A\right)$$
4	1 2 3	mpsyl	$$⊢A\in V\to \mathrm{I}\left(A\right)=A$$