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 ) |
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 ) |