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Metamath Proof Explorer

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	$⊢ x = y \to A = \{z \| [y/ x] z \in A\}$

Proof

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