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 -> A = { z | [ y / x ] z e. A } )

Proof

Step	Hyp	Ref	Expression
1		sbequ12	|- ( x = y -> ( z e. A <-> [ y / x ] z e. A ) )
2	1	eqabdv	|- ( x = y -> A = { z | [ y / x ] z e. A } )