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 )