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Metamath Proof Explorer

Theorem csbeq1a

Description: Equality theorem for proper substitution into a class. (Contributed by NM, 10-Nov-2005)

		Ref	Expression
	Assertion	csbeq1a	$⊢ x = A \to B = ⦋ A / x ⦌ B$

Step	Hyp	Ref	Expression
1		csbid	$⊢ ⦋ x / x ⦌ B = B$
2		csbeq1	$⊢ x = A \to ⦋ x / x ⦌ B = ⦋ A / x ⦌ B$
3	1 2	eqtr3id	$⊢ x = A \to B = ⦋ A / x ⦌ B$