Theorem nexd 1771

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

Hypotheses

Ref	Expression
nexd.1	⊢ Ⅎxφ
nexd.2	⊢ (φ → ¬ ψ)

Assertion

Ref	Expression
nexd	⊢ (φ → ¬ ∃xψ)

Proof of Theorem nexd

Step	Hyp	Ref	Expression
1		nexd.1	. . 3 ⊢ Ⅎxφ
2	1	nfri 1762	. 2 ⊢ (φ → ∀xφ)
3		nexd.2	. 2 ⊢ (φ → ¬ ψ)
4	2, 3	nexdh 1589	1 ⊢ (φ → ¬ ∃xψ)

Syntax hints:  ¬ wn 3   → wi 4  ∃wex 1541  Ⅎwnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is referenced by:  nexdv  1916