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Proof step 1 from proof ext-setequal (conclusion)

⊦ x ≡ y ↔ (∀ a. a ∈ x ↔ a ∈ y)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ x ≡ y ↔ ¬ ¬(x ⊆ y ∧ y ⊆ x)
Proof step 3:
⊦ ¬ ¬(x ⊆ y ∧ y ⊆ x) ↔ (∀ a. a ∈ x ↔ a ∈ y)

Rule argument

spec: inst: name: setequal-def seq: ⊦ x ≡ y ↔ ¬ ¬(x ⊆ y ∧ y ⊆ x) subst: [y, x] → [y, x] flags: rewrite, current

Additional information

Used terms: y, x