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Metamath Proof Explorer

Theorem 19.37v

Description: Version of 19.37 with a disjoint variable condition, requiring fewer axioms. (Contributed by NM, 21-Jun-1993)

Ref Expression
Assertion 19.37v ⊢ ∃ x φ → ψ ↔ φ → ∃ x ψ

Proof

Step Hyp Ref Expression
1 19.35 ⊢ ∃ x φ → ψ ↔ ∀ x φ → ∃ x ψ
2 19.3v ⊢ ∀ x φ ↔ φ
3 2 imbi1i ⊢ ∀ x φ → ∃ x ψ ↔ φ → ∃ x ψ
4 1 3 bitri ⊢ ∃ x φ → ψ ↔ φ → ∃ x ψ