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Metamath Proof Explorer

Theorem uneq12

Description: Equality theorem for the union of two classes. (Contributed by NM, 29-Mar-1998)

		Ref	Expression
	Assertion	uneq12	$⊢ (A = B \land C = D) \to A \cup C = B \cup D$

Step	Hyp	Ref	Expression
1		uneq1	$⊢ A = B \to A \cup C = B \cup C$
2		uneq2	$⊢ C = D \to B \cup C = B \cup D$
3	1 2	sylan9eq	$⊢ (A = B \land C = D) \to A \cup C = B \cup D$