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Metamath Proof Explorer

Theorem exdistr

Description: Distribution of existential quantifiers. See also exdistrv . (Contributed by NM, 9-Mar-1995)

Ref Expression
Assertion exdistr ⊢ ∃ x ∃ y φ ∧ ψ ↔ ∃ x φ ∧ ∃ y ψ

Proof

Step Hyp Ref Expression
1 19.42v ⊢ ∃ y φ ∧ ψ ↔ φ ∧ ∃ y ψ
2 1 exbii ⊢ ∃ x ∃ y φ ∧ ψ ↔ ∃ x φ ∧ ∃ y ψ