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Metamath Proof Explorer

Theorem bj-alexim

Description: Closed form of aleximi . Note: this proof is shorter, so aleximi could be deduced from it ( exim would have to be proved first, see bj-eximALT but its proof is shorter (currently almost a subproof of aleximi )). (Contributed by BJ, 8-Nov-2021)

Ref Expression
Assertion bj-alexim ⊢ ∀ x φ → ψ → χ → ∀ x φ → ∃ x ψ → ∃ x χ

Proof

Step Hyp Ref Expression
1 alim ⊢ ∀ x φ → ψ → χ → ∀ x φ → ∀ x ψ → χ
2 exim ⊢ ∀ x ψ → χ → ∃ x ψ → ∃ x χ
3 1 2 syl6 ⊢ ∀ x φ → ψ → χ → ∀ x φ → ∃ x ψ → ∃ x χ