Description: Equality theorem for indexed intersection. (Contributed by Glauco Siliprandi, 8-Apr-2021)
Ref | Expression | ||
---|---|---|---|
Hypothesis | iineq1d.1 | |- ( ph -> A = B ) |
|
Assertion | iineq1d | |- ( ph -> |^|_ x e. A C = |^|_ x e. B C ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iineq1d.1 | |- ( ph -> A = B ) |
|
2 | iineq1 | |- ( A = B -> |^|_ x e. A C = |^|_ x e. B C ) |
|
3 | 1 2 | syl | |- ( ph -> |^|_ x e. A C = |^|_ x e. B C ) |