Theorem esumeq2sdv

Description: Equality deduction for extended sum. (Contributed by Thierry Arnoux, 25-Dec-2016)

	Ref	Expression
Hypothesis	esumeq2sdv.1	$$⊢\phi \to B=C$$
Assertion	esumeq2sdv	$$⊢\phi \to \underset{k\in A}{{\sum }^{*}}B=\underset{k\in A}{{\sum }^{*}}C$$

Proof

Step	Hyp	Ref	Expression
1		esumeq2sdv.1	$$⊢\phi \to B=C$$
2	1	adantr	$$⊢\left(\phi \wedge k\in A\right)\to B=C$$
3	2	esumeq2dv	$$⊢\phi \to \underset{k\in A}{{\sum }^{*}}B=\underset{k\in A}{{\sum }^{*}}C$$