This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem eeanv

Description: Distribute a pair of existential quantifiers over a conjunction. Combination of 19.41v and 19.42v . For a version requiring fewer axioms but with additional disjoint variable conditions, see exdistrv . (Contributed by NM, 26-Jul-1995)

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

Proof

Step Hyp Ref Expression
1 nfv ⊢ Ⅎ y φ
2 nfv ⊢ Ⅎ x ψ
3 1 2 eean ⊢ ∃ x ∃ y φ ∧ ψ ↔ ∃ x φ ∧ ∃ y ψ