The equivalence and judgement for Weyl type theorems of a bounded linear operator T on a Hilbert space are discussed, a new spectrum σ2 (T) is defined in view of the consistency in Fredholm index. By using the relation between σ2 (T) and ρτ(T), the following conclusions are proved: Browder′s theorem holds for T if and only if ρτ(T)ρb(T)∪σ1(T) ∪σ2(T); T∈B(H) satisfies Weyl′s theorem if and only if π00(T)ρτ(T)ρb(T)∪σ1(T) ∪σ2(T), where ρb(T)={λ∈C: T-λ I is Browder},σ1(T) is a variant of the essential approximate point spectrum, and π00(T) denotes the set of all isolated eigenvalues of finite multiplicity; both T and T* satisfy a-Browder′s theorem if and only if ρτ(T)ρab(T)∪σ2(T)∪int σSF(T)∪ {λ∈C: des (T-λ I)

consistent Fredholm index operator; Weyl type theorem; spectrum