Let x0 of type ι be given.
Let x1 of type ι be given.
Apply ordinal_In_Or_Subq with
x0,
x1,
or (x0 ⊆ x1) (x1 ⊆ x0) leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Assume H2: x0 ∈ x1.
Apply orIL with
x0 ⊆ x1,
x1 ⊆ x0.
Apply ordinal_TransSet with
x1,
x0 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Assume H2: x1 ⊆ x0.
Apply orIR with
x0 ⊆ x1,
x1 ⊆ x0.
The subproof is completed by applying H2.