Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfbid Unicode version

Theorem nfbid 1933
 Description: If in a context is not free in and , it is not free in . (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 29-Dec-2017.)
Hypotheses
Ref Expression
nfbid.1
nfbid.2
Assertion
Ref Expression
nfbid

Proof of Theorem nfbid
StepHypRef Expression
1 dfbi2 628 . 2
2 nfbid.1 . . . 4
3 nfbid.2 . . . 4
42, 3nfimd 1917 . . 3
53, 2nfimd 1917 . . 3
64, 5nfand 1925 . 2
71, 6nfxfrd 1646 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  F/wnf 1616 This theorem is referenced by:  nfbi  1934  nfeud2  2296  nfeqd  2626  nfiotad  5559  iota2df  5580  axextnd  8987  axrepndlem1  8988  axrepndlem2  8989  axacndlem4  9009  axacndlem5  9010  axacnd  9011  axextdist  29232  wl-sb8eut  30022 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
 Copyright terms: Public domain W3C validator