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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: ordinal x0.
Assume H1: x0{(λ x3 . SetAdjoin x3 (Sing 1)) x2|x2 ∈ x1}.
Apply ReplE_impred with x1, λ x2 . (λ x3 . SetAdjoin x3 (Sing 1)) x2, x0, False leaving 2 subgoals.
The subproof is completed by applying H1.
Let x2 of type ι be given.
Assume H2: x2x1.
Assume H3: x0 = (λ x3 . SetAdjoin x3 (Sing 1)) x2.
Apply tagged_not_ordinal with x2.
Apply H3 with λ x3 x4 . ordinal x3.
The subproof is completed by applying H0.