Theorem iineq2i

Description: Equality inference for indexed intersection. (Contributed by NM, 22-Oct-2003)

	Ref	Expression
Hypothesis	iuneq2i.1	|- ( x e. A -> B = C )
Assertion	iineq2i	|- |^|_ x e. A B = |^|_ x e. A C

Proof

Step	Hyp	Ref	Expression
1		iuneq2i.1	|- ( x e. A -> B = C )
2		iineq2	|- ( A. x e. A B = C -> |^|_ x e. A B = |^|_ x e. A C )
3	2 1	mprg	|- |^|_ x e. A B = |^|_ x e. A C