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Metamath Proof Explorer

Theorem djueq1

Description: Equality theorem for disjoint union. (Contributed by Jim Kingdon, 23-Jun-2022)

		Ref	Expression
	Assertion	djueq1	$⊢ A = B \to (A ⊔︀ C) = (B ⊔︀ C)$

Step	Hyp	Ref	Expression
1		eqid	$⊢ C = C$
2		djueq12	$⊢ (A = B \land C = C) \to (A ⊔︀ C) = (B ⊔︀ C)$
3	1 2	mpan2	$⊢ A = B \to (A ⊔︀ C) = (B ⊔︀ C)$