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Metamath Proof Explorer

Theorem ineq2

Description: Equality theorem for intersection of two classes. (Contributed by NM, 26-Dec-1993)

		Ref	Expression
	Assertion	ineq2	$⊢ A = B \to C \cap A = C \cap B$

Step	Hyp	Ref	Expression
1		ineq1	$⊢ A = B \to A \cap C = B \cap C$
2		incom	$⊢ C \cap A = A \cap C$
3		incom	$⊢ C \cap B = B \cap C$
4	1 2 3	3eqtr4g	$⊢ A = B \to C \cap A = C \cap B$