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Metamath Proof Explorer

Theorem djueq2

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

		Ref	Expression
	Assertion	djueq2	$⊢ A = B \to (C ⊔︀ A) = (C ⊔︀ B)$

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