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Metamath Proof Explorer

Theorem ineq12

Description: Equality theorem for intersection of two classes. (Contributed by NM, 8-May-1994)

		Ref	Expression
	Assertion	ineq12	$⊢ (A = B \land C = D) \to A \cap C = B \cap D$

Step	Hyp	Ref	Expression
1		ineq1	$⊢ A = B \to A \cap C = B \cap C$
2		ineq2	$⊢ C = D \to B \cap C = B \cap D$
3	1 2	sylan9eq	$⊢ (A = B \land C = D) \to A \cap C = B \cap D$