diff --git a/base/array.jl b/base/array.jl
index a9c8e46b0de28..7cf0424513fce 100644
--- a/base/array.jl
+++ b/base/array.jl
@@ -85,7 +85,6 @@ UInt8
 ```
 """
 eltype(::Type) = Any
-eltype(::Type{Any}) = Any
 eltype(::Type{Bottom}) = throw(ArgumentError("Union{} does not have elements"))
 eltype(x) = eltype(typeof(x))
 
diff --git a/base/pointer.jl b/base/pointer.jl
index b0ded31b87a27..bbc5c215d38f2 100644
--- a/base/pointer.jl
+++ b/base/pointer.jl
@@ -143,8 +143,6 @@ function pointer_from_objref(@nospecialize(x))
     ccall(:jl_value_ptr, Ptr{Cvoid}, (Any,), x)
 end
 
-eltype(::Type{Ptr{T}}) where {T} = T
-
 ## limited pointer arithmetic & comparison ##
 
 ==(x::Ptr, y::Ptr) = UInt(x) == UInt(y)
diff --git a/stdlib/Dates/src/types.jl b/stdlib/Dates/src/types.jl
index d6ea6a875926f..a21ef5de353ef 100644
--- a/stdlib/Dates/src/types.jl
+++ b/stdlib/Dates/src/types.jl
@@ -339,7 +339,6 @@ Base.typemin(::Union{Date, Type{Date}}) = Date(-252522163911150, 1, 1)
 Base.typemax(::Union{Time, Type{Time}}) = Time(23, 59, 59, 999, 999, 999)
 Base.typemin(::Union{Time, Type{Time}}) = Time(0)
 # Date-DateTime promotion, isless, ==
-Base.eltype(::Type{T}) where {T<:Period} = T
 Base.promote_rule(::Type{Date}, x::Type{DateTime}) = DateTime
 Base.isless(x::T, y::T) where {T<:TimeType} = isless(value(x), value(y))
 Base.isless(x::TimeType, y::TimeType) = isless(promote(x, y)...)