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Metamath Proof Explorer

Theorem exbi

Description: Theorem 19.18 of Margaris p. 90. (Contributed by NM, 12-Mar-1993)

Ref Expression
Assertion exbi ⊢ ∀ x φ ↔ ψ → ∃ x φ ↔ ∃ x ψ

Proof

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