Let x0 of type ι be given.
Assume H2:
∀ x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ (x1 = x2 ⟶ ∀ x3 : ο . x3) ⟶ not (0aea9.. x1 x2).
Apply unknownprop_272808853bb51fe5bae430490a1fcfe5c7dccc89120d4626502b3fb9065edb74 with
x0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Let x1 of type ι be given.
Assume H3: x1 ∈ x0.
Let x2 of type ι be given.
Assume H4: x2 ∈ x0.
Assume H5: x1 = x2 ⟶ ∀ x3 : ο . x3.
Apply H2 with
x1,
x2 leaving 4 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
Apply unknownprop_331d7f66eeb37dc381bf2e3606d3b3c601f9b8768b689e8985564581b76a5fdc with
x1,
x2 leaving 3 subgoals.
Apply unknownprop_d970592334f635f8f9210ca498f17663c65d10424d394c992d89fdcf9b46fb0e with
x1.
Apply H0 with
x1.
The subproof is completed by applying H3.
Apply unknownprop_d970592334f635f8f9210ca498f17663c65d10424d394c992d89fdcf9b46fb0e with
x2.
Apply H0 with
x2.
The subproof is completed by applying H4.
The subproof is completed by applying H6.