Let x0 of type ι be given.
Let x1 of type ι be given.
Apply H0 with
ordinal (binunion x0 x1).
Assume H3:
∀ x2 . x2 ∈ x0 ⟶ TransSet x2.
Apply H1 with
ordinal (binunion x0 x1).
Assume H5:
∀ x2 . x2 ∈ x1 ⟶ TransSet x2.
Apply ordinal_linear with
x0,
x1,
ordinal (binunion x0 x1) leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply Subq_binunion_eq with
x0,
x1,
λ x2 x3 : ο . x3 ⟶ ordinal (binunion x0 x1).
Apply H6 with
λ x2 x3 . ordinal x3.
The subproof is completed by applying H1.
Apply Subq_binunion_eq with
x1,
x0,
λ x2 x3 : ο . x3 ⟶ ordinal (binunion x0 x1).
Apply binunion_com with
x1,
x0,
λ x2 x3 . x3 = x0 ⟶ ordinal (binunion x0 x1).
Apply H6 with
λ x2 x3 . ordinal x3.
The subproof is completed by applying H0.