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Metamath Proof Explorer

Theorem 19.39

Description: Theorem 19.39 of Margaris p. 90. (Contributed by NM, 12-Mar-1993)

Ref Expression
Assertion 19.39 ⊢ ∃ x φ → ∃ x ψ → ∃ x φ → ψ

Proof

Step Hyp Ref Expression
1 19.2 ⊢ ∀ x φ → ∃ x φ
2 1 imim1i ⊢ ∃ 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