Metamath Proof Explorer

Theorem 19.36vv

Description: Theorem *11.43 in WhiteheadRussell p. 163. Theorem 19.36 of Margaris p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 25-May-2011)

Ref Expression
Assertion 19.36vv ⊢ ∃ x ∃ y φ → ψ ↔ ∀ x ∀ y φ → ψ

Proof

Step Hyp Ref Expression
1 19.36v ⊢ ∃ y φ → ψ ↔ ∀ y φ → ψ
2 1 exbii ⊢ ∃ x ∃ y φ → ψ ↔ ∃ x ∀ y φ → ψ
3 19.36v ⊢ ∃ x ∀ y φ → ψ ↔ ∀ x ∀ y φ → ψ
4 2 3 bitri ⊢ ∃ x ∃ y φ → ψ ↔ ∀ x ∀ y φ → ψ