Theorem ideq

Description: For sets, the identity relation is the same as equality. (Contributed by NM, 13-Aug-1995)

	Ref	Expression
Hypothesis	ideq.1	$$⊢B\in \mathrm{V}$$
Assertion	ideq	$$⊢A\mathrm{I}B\leftrightarrow A=B$$

Proof

Step	Hyp	Ref	Expression
1		ideq.1	$$⊢B\in \mathrm{V}$$
2		ideqg	$$⊢B\in \mathrm{V}\to \left(A\mathrm{I}B\leftrightarrow A=B\right)$$
3	1 2	ax-mp	$$⊢A\mathrm{I}B\leftrightarrow A=B$$