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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 )