Theorem sbab

Description: The right-hand side of the second equality is a way of representing proper substitution of y for x into a class variable. (Contributed by NM, 14-Sep-2003)

	Ref	Expression
Assertion	sbab	$$⊢x=y\to A=\left\{z|\left[y/x\right]z\in A\right\}$$

Proof

Step	Hyp	Ref	Expression
1		sbequ12	$$⊢x=y\to \left(z\in A\leftrightarrow \left[y/x\right]z\in A\right)$$
2	1	abbi2dv	$$⊢x=y\to A=\left\{z|\left[y/x\right]z\in A\right\}$$