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SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
Mathbox for BJ
First-order logic
Adding ax-5
bj-cbveximi
Metamath Proof Explorer
Description: An equality-free general instance of one half of a precise form of
bj-cbvex . (Contributed by BJ , 12-Mar-2023)
(Proof modification is discouraged.)
Ref
Expression
Hypotheses
bj-cbvalimi.maj
⊢ χ → φ → ψ
bj-cbveximi.denote
⊢ ∀ x ∃ y χ
Assertion
bj-cbveximi
⊢ ∃ x φ → ∃ y ψ
Proof
Step
Hyp
Ref
Expression
1
bj-cbvalimi.maj
⊢ χ → φ → ψ
2
bj-cbveximi.denote
⊢ ∀ x ∃ y χ
3
1
gen2
⊢ ∀ x ∀ y χ → φ → ψ
4
bj-cbvexim
⊢ ∀ x ∃ y χ → ∀ x ∀ y χ → φ → ψ → ∃ x φ → ∃ y ψ
5
2 3 4
mp2
⊢ ∃ x φ → ∃ y ψ