Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H0: x0 ⊆ x2.
Assume H1: x1 ⊆ x2.
Let x3 of type ι be given.
Apply binunionE with
x0,
x1,
x3,
x3 ∈ x2 leaving 3 subgoals.
The subproof is completed by applying H2.
Assume H3: x3 ∈ x0.
Apply H0 with
x3.
The subproof is completed by applying H3.
Assume H3: x3 ∈ x1.
Apply H1 with
x3.
The subproof is completed by applying H3.