Description: Equality deduction for indexed union. (Contributed by NM, 3-Aug-2004)
Ref | Expression | ||
---|---|---|---|
Hypothesis | iuneq2dv.1 | |- ( ( ph /\ x e. A ) -> B = C ) |
|
Assertion | iuneq2dv | |- ( ph -> U_ x e. A B = U_ x e. A C ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iuneq2dv.1 | |- ( ( ph /\ x e. A ) -> B = C ) |
|
2 | 1 | ralrimiva | |- ( ph -> A. x e. A B = C ) |
3 | iuneq2 | |- ( A. x e. A B = C -> U_ x e. A B = U_ x e. A C ) |
|
4 | 2 3 | syl | |- ( ph -> U_ x e. A B = U_ x e. A C ) |