Theorem nexdv 983

Description: Deduction for generalization rule for negated wff.

Hypothesis

Ref	Expression
nexdv.1	⊢ (φ → ¬ ψ)

Assertion

Ref	Expression
nexdv	⊢ (φ → ¬ ∃xψ)

Distinct variable group(s):   φ,x

Proof of Theorem nexdv

Step	Hyp	Ref	Expression
1		ax-17 925	. 2 ⊢ (φ → ∀xφ)
2		nexdv.1	. 2 ⊢ (φ → ¬ ψ)
3	1, 2	nexd 780	1 ⊢ (φ → ¬ ∃xψ)

Syntax hints:  ¬ wn 1   → wi 2  ∃wex 678

This theorem is referenced by:  sbc2or 1454  imasn 2616  fvprc 2829  genpnnp 3902

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677  ax-17 925

This theorem depends on definitions:  df-bi 128  df-ex 679

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