Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H0: x2 ⊆ x0.
Assume H1: x2 ⊆ x1.
Let x3 of type ι be given.
Assume H2: x3 ∈ x2.
Apply binintersectI with
x0,
x1,
x3 leaving 2 subgoals.
Apply H0 with
x3.
The subproof is completed by applying H2.
Apply H1 with
x3.
The subproof is completed by applying H2.