Metamath Proof Explorer


Theorem iineq2dv

Description: Equality deduction for indexed intersection. (Contributed by NM, 3-Aug-2004)

Ref Expression
Hypothesis iuneq2dv.1
|- ( ( ph /\ x e. A ) -> B = C )
Assertion iineq2dv
|- ( ph -> |^|_ x e. A B = |^|_ x e. A C )

Proof

Step Hyp Ref Expression
1 iuneq2dv.1
 |-  ( ( ph /\ x e. A ) -> B = C )
2 nfv
 |-  F/ x ph
3 2 1 iineq2d
 |-  ( ph -> |^|_ x e. A B = |^|_ x e. A C )