Theorem iuneq1i

Description: Equality theorem for indexed union. (Contributed by Glauco Siliprandi, 3-Mar-2021)

	Ref	Expression
Hypothesis	iuneq1i.1	$$⊢A=B$$
Assertion	iuneq1i	$$⊢\bigcup _{x\in A}C=\bigcup _{x\in B}C$$

Proof

Step	Hyp	Ref	Expression
1		iuneq1i.1	$$⊢A=B$$
2		iuneq1	$$⊢A=B\to \bigcup _{x\in A}C=\bigcup _{x\in B}C$$
3	1 2	ax-mp	$$⊢\bigcup _{x\in A}C=\bigcup _{x\in B}C$$