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Proof step 7 from proof rm-in-01 (previous step)

a ∈ (a0 ∈ x0 ⊃ rmdup(x0);a0 ' + rmdup(x0)), ∀ a. a ∈ rmdup(x0) → a ∈ x0 ⊦ a = a0, a ∈ x0

User applied rule case distinction

And obtained the following new goals

Proof step 8:
a ∈ rmdup(x0), a0 ∈ x0, ∀ a. a ∈ rmdup(x0) → a ∈ x0 ⊦ a = a0, a ∈ x0
Proof step 10:
a ∈ a0 ' + rmdup(x0), ∀ a. a ∈ rmdup(x0) → a ∈ x0 ⊦ a = a0, a ∈ x0, a0 ∈ x0

Rule argument

pos: left 1

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