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Metamath Proof Explorer

Theorem 19.40-2

Description: Theorem *11.42 in WhiteheadRussell p. 163. Theorem 19.40 of Margaris p. 90 with two quantifiers. (Contributed by Andrew Salmon, 24-May-2011)

Ref Expression
Assertion 19.40-2 ⊢ ∃ x ∃ y φ ∧ ψ → ∃ x ∃ y φ ∧ ∃ x ∃ y ψ

Proof

Step Hyp Ref Expression
1 19.40 ⊢ ∃ y φ ∧ ψ → ∃ y φ ∧ ∃ y ψ
2 1 eximi ⊢ ∃ x ∃ y φ ∧ ψ → ∃ x ∃ y φ ∧ ∃ y ψ
3 19.40 ⊢ ∃ x ∃ y φ ∧ ∃ y ψ → ∃ x ∃ y φ ∧ ∃ x ∃ y ψ
4 2 3 syl ⊢ ∃ x ∃ y φ ∧ ψ → ∃ x ∃ y φ ∧ ∃ x ∃ y ψ