Theorem djueq1

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

	Ref	Expression
Assertion	djueq1	$$⊢A=B\to \left(A\mathrm{\bigsqcup ︀}C\right)=\left(B\mathrm{\bigsqcup ︀}C\right)$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢C=C$$
2		djueq12	$$⊢\left(A=B\wedge C=C\right)\to \left(A\mathrm{\bigsqcup ︀}C\right)=\left(B\mathrm{\bigsqcup ︀}C\right)$$
3	1 2	mpan2	$$⊢A=B\to \left(A\mathrm{\bigsqcup ︀}C\right)=\left(B\mathrm{\bigsqcup ︀}C\right)$$