Metamath Proof Explorer

Theorem 19.26-2

Description: Theorem 19.26 with two quantifiers. (Contributed by NM, 3-Feb-2005)

Ref Expression
Assertion 19.26-2 ⊢ ∀ x ∀ y φ ∧ ψ ↔ ∀ x ∀ y φ ∧ ∀ x ∀ y ψ

Proof

Step Hyp Ref Expression
1 19.26 ⊢ ∀ y φ ∧ ψ ↔ ∀ y φ ∧ ∀ y ψ
2 1 albii ⊢ ∀ x ∀ y φ ∧ ψ ↔ ∀ x ∀ y φ ∧ ∀ y ψ
3 19.26 ⊢ ∀ x ∀ y φ ∧ ∀ y ψ ↔ ∀ x ∀ y φ ∧ ∀ x ∀ y ψ
4 2 3 bitri ⊢ ∀ x ∀ y φ ∧ ψ ↔ ∀ x ∀ y φ ∧ ∀ x ∀ y ψ