Theorem iuneq1d

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

	Ref	Expression
Hypothesis	iuneq1d.1	|- ( ph -> A = B )
Assertion	iuneq1d	|- ( ph -> U_ x e. A C = U_ x e. B C )

Proof

Step	Hyp	Ref	Expression
1		iuneq1d.1	|- ( ph -> A = B )
2		iuneq1	|- ( A = B -> U_ x e. A C = U_ x e. B C )
3	1 2	syl	|- ( ph -> U_ x e. A C = U_ x e. B C )