Metamath Proof Explorer

Theorem 19.28vv

Description: Theorem *11.47 in WhiteheadRussell p. 164. Theorem 19.28 of Margaris p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011)

Ref Expression
Assertion 19.28vv ⊢ ∀ x ∀ y ψ ∧ φ ↔ ψ ∧ ∀ x ∀ y φ

Proof

Step Hyp Ref Expression
1 19.28v ⊢ ∀ y ψ ∧ φ ↔ ψ ∧ ∀ y φ
2 1 albii ⊢ ∀ x ∀ y ψ ∧ φ ↔ ∀ x ψ ∧ ∀ y φ
3 19.28v ⊢ ∀ x ψ ∧ ∀ y φ ↔ ψ ∧ ∀ x ∀ y φ
4 2 3 bitri ⊢ ∀ x ∀ y ψ ∧ φ ↔ ψ ∧ ∀ x ∀ y φ