NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  nexdv GIF version

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
StepHypRef Expression
1 nfv 1619 . 2 xφ
2 nexdv.1 . 2 (φ → ¬ ψ)
31, 2nexd 1771 1 (φ → ¬ xψ)
Colors of variables: wff setvar class
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  3054
  Copyright terms: Public domain W3C validator