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Proofgold Proof

pf
Let x0 of type ο be given.
Let x1 of type ο be given.
Let x2 of type ο be given.
Apply and_def with λ x3 x4 : ο → ο → ο . x4 (x4 x0 x1) x2∀ x5 : ο . (x0x1x2x5)x5.
Assume H0: ∀ x3 : ο . ((∀ x4 : ο . (x0x1x4)x4)x2x3)x3.
Let x3 of type ο be given.
Assume H1: x0x1x2x3.
Apply H0 with x3.
Assume H2: ∀ x4 : ο . (x0x1x4)x4.
Assume H3: x2.
Apply H2 with x3.
Assume H4: x0.
Assume H5: x1.
Apply H1 leaving 3 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
The subproof is completed by applying H3.