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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ιι be given.
Assume H0: ∀ x3 . x3x0x2 x3x1.
Assume H1: ∀ x3 . x3x0∀ x4 . x4x0x2 x3 = x2 x4x3 = x4.
Assume H2: ∀ x3 . x3x1∃ x4 . and (x4x0) (x2 x4 = x3).
Apply and3I with ∀ x3 . x3x0x2 x3x1, ∀ x3 . x3x0∀ x4 . x4x0x2 x3 = x2 x4x3 = x4, ∀ x3 . x3x1∃ x4 . and (x4x0) (x2 x4 = x3) leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.