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Proof step 5 from proof ext-setequal (previous step)

⊦ (∀ a. a ∈ x → a ∈ y) ∧ y ⊆ x ↔ (∀ a. a ∈ x ↔ a ∈ y)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ x ⊆ y ↔ (∀ a. a ∈ x → a ∈ y)
Proof step 7:
⊦ (∀ a. a ∈ x → a ∈ y) ∧ (∀ a. a ∈ y → a ∈ x) ↔ (∀ a. a ∈ x ↔ a ∈ y)

Rule argument

spec: list-set name: subset seq: ⊦ x ⊆ y ↔ (∀ a. a ∈ x → a ∈ y) subst: [y, x] → [x, y] flags: <all paths>

Additional information

Used terms: x, y