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Metamath Proof Explorer

Theorem 19.24

Description: Theorem 19.24 of Margaris p. 90. (Contributed by NM, 12-Mar-1993)

Ref Expression
Assertion 19.24 ⊢ ∀ x φ → ∀ x ψ → ∃ x φ → ψ

Proof

Step Hyp Ref Expression
1 19.2 ⊢ ∀ x ψ → ∃ x ψ
2 1 imim2i ⊢ ∀ x φ → ∀ x ψ → ∀ x φ → ∃ x ψ
3 19.35 ⊢ ∃ x φ → ψ ↔ ∀ x φ → ∃ x ψ
4 2 3 sylibr ⊢ ∀ x φ → ∀ x ψ → ∃ x φ → ψ