Theorem iuneq12d

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

	Ref	Expression
Hypotheses	iuneq1d.1	|- ( ph -> A = B )
	iuneq12d.2	|- ( ph -> C = D )
Assertion	iuneq12d	|- ( ph -> U_ x e. A C = U_ x e. B D )

Proof

Step	Hyp	Ref	Expression
1		iuneq1d.1	|- ( ph -> A = B )
2		iuneq12d.2	|- ( ph -> C = D )
3	1	iuneq1d	|- ( ph -> U_ x e. A C = U_ x e. B C )
4	2	adantr	|- ( ( ph /\ x e. B ) -> C = D )
5	4	iuneq2dv	|- ( ph -> U_ x e. B C = U_ x e. B D )
6	3 5	eqtrd	|- ( ph -> U_ x e. A C = U_ x e. B D )