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Metamath Proof Explorer

Theorem 19.23vv

Description: Theorem 19.23v extended to two variables. (Contributed by NM, 10-Aug-2004)

Ref Expression
Assertion 19.23vv ⊢ ∀ x ∀ y φ → ψ ↔ ∃ x ∃ y φ → ψ

Proof

Step Hyp Ref Expression
1 19.23v ⊢ ∀ y φ → ψ ↔ ∃ y φ → ψ
2 1 albii ⊢ ∀ x ∀ y φ → ψ ↔ ∀ x ∃ y φ → ψ
3 19.23v ⊢ ∀ x ∃ y φ → ψ ↔ ∃ x ∃ y φ → ψ
4 2 3 bitri ⊢ ∀ x ∀ y φ → ψ ↔ ∃ x ∃ y φ → ψ