Let x0 of type ι be given.

Let x1 of type ι → ο be given.

Let x2 of type ι → ο be given.

Let x3 of type ι → ο be given.

Assume H0: PNoEq_ x0 x1 x2.

Assume H1: PNoEq_ x0 x2 x3.

Let x4 of type ι be given.

Assume H2: x4 ∈ x0.

Apply iff_trans with x1 x4, x2 x4, x3 x4 leaving 2 subgoals.

Apply H0 with x4.

The subproof is completed by applying H2.

Apply H1 with x4.

The subproof is completed by applying H2.

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Proofgold Proof