Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply PNoLt_tra with
SNoLev x0,
SNoLev x1,
SNoLev x2,
λ x3 . x3 ∈ x0,
λ x3 . x3 ∈ x1,
λ x3 . x3 ∈ x2 leaving 5 subgoals.
Apply SNoLev_ordinal with
x0.
The subproof is completed by applying H0.
Apply SNoLev_ordinal with
x1.
The subproof is completed by applying H1.
Apply SNoLev_ordinal with
x2.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.