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Metamath Proof Explorer

Theorem exim

Description: Theorem 19.22 of Margaris p. 90. (Contributed by NM, 10-Jan-1993) (Proof shortened by Wolf Lammen, 4-Jul-2014)

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

Proof

Step Hyp Ref Expression
1 id ⊢ φ → ψ → φ → ψ
2 1 aleximi ⊢ ∀ x φ → ψ → ∃ x φ → ∃ x ψ