Theorem nexdv 1916

Description: Deduction for generalization rule for negated wff. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
nexdv.1	⊢ (φ → ¬ ψ)

Assertion

Ref	Expression
nexdv	⊢ (φ → ¬ ∃xψ)

Distinct variable group:   φ,x

Allowed substitution hint:   ψ(x)

Proof of Theorem nexdv

Step	Hyp	Ref	Expression
1		nfv 1619	. 2 ⊢ Ⅎxφ
2		nexdv.1	. 2 ⊢ (φ → ¬ ψ)
3	1, 2	nexd 1771	1 ⊢ (φ → ¬ ∃xψ)

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

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:  sbc2or  3055