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Metamath Proof Explorer

Theorem 19.25

Description: Theorem 19.25 of Margaris p. 90. (Contributed by NM, 12-Mar-1993)

Ref Expression
Assertion 19.25 ⊢ ∀ y ∃ x φ → ψ → ∃ y ∀ x φ → ∃ y ∃ x ψ

Proof

Step Hyp Ref Expression
1 19.35 ⊢ ∃ x φ → ψ ↔ ∀ x φ → ∃ x ψ
2 1 biimpi ⊢ ∃ x φ → ψ → ∀ x φ → ∃ x ψ
3 2 aleximi ⊢ ∀ y ∃ x φ → ψ → ∃ y ∀ x φ → ∃ y ∃ x ψ