Proofgold Proof

pf
Apply andI with TransSet 0, ∀ x0 . x0 ∈ 0 ⟶ TransSet x0 leaving 2 subgoals. Let x0 of type ι be given. Assume H0: x0 ∈ 0. Apply FalseE with x0 ⊆ 0. Apply EmptyE with x0. The subproof is completed by applying H0. Let x0 of type ι be given. Assume H0: x0 ∈ 0. Apply FalseE with TransSet x0. Apply EmptyE with x0. The subproof is completed by applying H0. ■