Theorem iuneq2d

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

	Ref	Expression
Hypothesis	iuneq2d.2	$$⊢\phi \to B=C$$
Assertion	iuneq2d	$$⊢\phi \to \bigcup _{x\in A}B=\bigcup _{x\in A}C$$

Proof

Step	Hyp	Ref	Expression
1		iuneq2d.2	$$⊢\phi \to B=C$$
2	1	adantr	$$⊢\left(\phi \wedge x\in A\right)\to B=C$$
3	2	iuneq2dv	$$⊢\phi \to \bigcup _{x\in A}B=\bigcup _{x\in A}C$$