Let x0 of type ι be given.

Let x1 of type ι → ι → ι be given.

Let x2 of type ι → ι → ι be given.

Let x3 of type ι → ι → ο be given.

Let x4 of type ι → ι → ο be given.

Assume H0: ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x1 x5 x6 = x2 x5 x6.

Assume H1: ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ iff (x3 x5 x6) (x4 x5 x6).

Claim L2: eb53d.. x0 x1 = eb53d.. x0 x2

Apply unknownprop_dbb26cd650ab4f49eb7a56474ebdc3b4a46f79fd66ae7129c609d055a8e1a150 with x0, x1, x2.

The subproof is completed by applying H0.

Claim L3: d2155.. x0 x3 = d2155.. x0 x4

Apply unknownprop_75d5b46497f20dc30e2e5351a60197c4fa9d445bc23c6c8245597bb858180907 with x0, x3, x4.

The subproof is completed by applying H1.

Let x5 of type ι → ι → ο be given.

The subproof is completed by applying H4.

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Proofgold Proof