Theorem djueq2

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

	Ref	Expression
Assertion	djueq2	⊢ ( 𝐴 = 𝐵 → ( 𝐶 ⊔ 𝐴 ) = ( 𝐶 ⊔ 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ 𝐶 = 𝐶
2		djueq12	⊢ ( ( 𝐶 = 𝐶 ∧ 𝐴 = 𝐵 ) → ( 𝐶 ⊔ 𝐴 ) = ( 𝐶 ⊔ 𝐵 ) )
3	1 2	mpan	⊢ ( 𝐴 = 𝐵 → ( 𝐶 ⊔ 𝐴 ) = ( 𝐶 ⊔ 𝐵 ) )