Theorem djueq2

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

	Ref	Expression
Assertion	djueq2	$$⊢A=B\to \left(C\mathrm{\bigsqcup ︀}A\right)=\left(C\mathrm{\bigsqcup ︀}B\right)$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢C=C$$
2		djueq12	$$⊢\left(C=C\wedge A=B\right)\to \left(C\mathrm{\bigsqcup ︀}A\right)=\left(C\mathrm{\bigsqcup ︀}B\right)$$
3	1 2	mpan	$$⊢A=B\to \left(C\mathrm{\bigsqcup ︀}A\right)=\left(C\mathrm{\bigsqcup ︀}B\right)$$