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Metamath Proof Explorer

Theorem nexd

Description: Deduction for generalization rule for negated wff. (Contributed by Mario Carneiro, 24-Sep-2016)

Ref Expression
Hypotheses nexd.1 ⊢ Ⅎ x φ
nexd.2 ⊢ φ → ¬ ψ
Assertion nexd ⊢ φ → ¬ ∃ x ψ

Proof

Step Hyp Ref Expression
1 nexd.1 ⊢ Ⅎ x φ
2 nexd.2 ⊢ φ → ¬ ψ
3 1 nf5ri ⊢ φ → ∀ x φ
4 3 2 nexdh ⊢ φ → ¬ ∃ x ψ