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

Theorem nfrd 1763
Description: Consequence of the definition of not-free in a context. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfrd.1 (φ → Ⅎxψ)
Assertion
Ref Expression
nfrd (φ → (ψxψ))

Proof of Theorem nfrd
StepHypRef Expression
1 nfrd.1 . 2 (φ → Ⅎxψ)
2 nfr 1761 . 2 (Ⅎxψ → (ψxψ))
31, 2syl 15 1 (φ → (ψxψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1540  wnf 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:  alrimdd  1768  nfim1  1811  nfim1OLD  1812  hbimd  1815  nfald  1852  19.9tOLD  1857  19.21tOLD  1863  nfan1  1881  cbv1  1979  cbv2  1981  sbied  2036  sbal1  2126  abidnf  3005
  Copyright terms: Public domain W3C validator