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 )