Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: x1 ⊆ x0.
Let x2 of type ι be given.
Assume H1: x2 ⊆ x0.
Assume H2: ∀ x3 . x3 ∈ x0 ⟶ x3 ∈ x1 ⟶ x3 ∈ x2.
Assume H3: ∀ x3 . x3 ∈ x0 ⟶ x3 ∈ x2 ⟶ x3 ∈ x1.
Apply set_ext with
x1,
x2 leaving 2 subgoals.
Let x3 of type ι be given.
Assume H4: x3 ∈ x1.
Apply H2 with
x3 leaving 2 subgoals.
Apply H0 with
x3.
The subproof is completed by applying H4.
The subproof is completed by applying H4.
Let x3 of type ι be given.
Assume H4: x3 ∈ x2.
Apply H3 with
x3 leaving 2 subgoals.
Apply H1 with
x3.
The subproof is completed by applying H4.
The subproof is completed by applying H4.