Theorem iuneq1d

Description: Equality theorem for indexed union, deduction version. (Contributed by Drahflow, 22-Oct-2015)

	Ref	Expression
Hypothesis	iuneq1d.1	$$⊢\phi \to A=B$$
Assertion	iuneq1d	$$⊢\phi \to \bigcup _{x\in A}C=\bigcup _{x\in B}C$$

Proof

Step	Hyp	Ref	Expression
1		iuneq1d.1	$$⊢\phi \to A=B$$
2		iuneq1	$$⊢A=B\to \bigcup _{x\in A}C=\bigcup _{x\in B}C$$
3	1 2	syl	$$⊢\phi \to \bigcup _{x\in A}C=\bigcup _{x\in B}C$$