Let x0 of type ο be given.
Let x1 of type (((ι → ο) → ο) → ο) → ο be given.
Let x2 of type (((ι → ο) → ο) → ο) → ο be given.
Apply functional extensionality with
eb5c9.. x0 x1 x2,
x2.
Let x3 of type ((ι → ο) → ο) → ο be given.
Apply prop_ext_2 with
eb5c9.. x0 x1 x2 x3,
x2 x3 leaving 2 subgoals.
Assume H1:
and (x0 ⟶ x1 x3) (not x0 ⟶ x2 x3).
Apply unknownprop_896ccc9f209efa8a895211d65adb5a90348b419f100f6ab5e9762ce4d7fa9cc1 with
x0 ⟶ x1 x3,
not x0 ⟶ x2 x3 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
Assume H1: x2 x3.
Apply unknownprop_389e2fb1855352fcc964ea44fe6723d7a1c2d512f04685300e3e97621725b977 with
x0 ⟶ x1 x3,
not x0 ⟶ x2 x3 leaving 2 subgoals.
Assume H2: x0.
Apply FalseE with
x1 x3.
Apply notE with
x0 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H1.