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Metamath Proof Explorer

Theorem exlimddv

Description: Existential elimination rule of natural deduction (Rule C, explained in exlimiv ). (Contributed by Mario Carneiro, 15-Jun-2016)

Ref Expression
Hypotheses exlimddv.1 ⊢ φ → ∃ x ψ
exlimddv.2 ⊢ φ ∧ ψ → χ
Assertion exlimddv ⊢ φ → χ

Proof

Step Hyp Ref Expression
1 exlimddv.1 ⊢ φ → ∃ x ψ
2 exlimddv.2 ⊢ φ ∧ ψ → χ
3 2 ex ⊢ φ → ψ → χ
4 3 exlimdv ⊢ φ → ∃ x ψ → χ
5 1 4 mpd ⊢ φ → χ